Ivo Babuška

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Ivo Babuška is affiliated with the following schools: University of Maryland, College Park, University of Texas at Austin, Charles University, Czech Technical University in Prague

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Ivo Babuška

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Mathematics

Why Is Ivo Babuška Influential?

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According to Wikipedia, Ivo M. Babuška was a Czech-American mathematician, noted for his studies of the finite element method and the proof of the Babuška–Lax–Milgram theorem in partial differential equations. One of the celebrated result in the finite elements is the so-called Ladyzenskaja–Babuška–Brezzi condition , which provides sufficient conditions for a stable mixed formulation. The LBB condition has guided mathematicians and engineers to develop state-of-the-art formulations for many technologically important problems like Darcy flow, Stokes flow, incompressible Navier–Stokes, nearly incompressible elasticity.

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Ivo Babuška's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The partition of unity finite element method: Basic theory and applications (1996) (3300)
The Partition of Unity Method (1997) (2399)
Finite Element Analysis (2021) (1730)
The finite element method with Lagrangian multipliers (1973) (1581)
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007) (1548)
A‐posteriori error estimates for the finite element method (1978) (1244)
Error-bounds for finite element method (1971) (1023)
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004) (904)
The design and analysis of the Generalized Finite Element Method (2000) (897)
The finite element method and its reliability (2001) (824)
ON THE ANGLE CONDITION IN THE FINITE ELEMENT METHOD (1976) (728)
Special finite element methods for a class of second order elliptic problems with rough coefficients (1994) (652)
The generalized finite element method (2001) (640)
Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM☆ (1995) (618)
Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers? (1997) (610)
Generalized finite element methods for three-dimensional structural mechanics problems (2000) (585)
The h-p version of the finite element method (1986) (529)
A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis (1983) (528)
A DiscontinuoushpFinite Element Method for Diffusion Problems (1998) (518)
The p-Version of the Finite Element Method for Parabolic Equations. Part 1 (1981) (517)
The Finite Element Method with Penalty (1973) (503)
The h-p version of the finite element method (1986) (499)
Solution of stochastic partial differential equations using Galerkin finite element techniques (2001) (470)
Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods (1983) (447)
The p and h-p Versions of the Finite Element Method, Basic Principles and Properties (1994) (446)
A Generalized Finite Element Method for solving the Helmholtz equation in two dimensions with minimal pollution (1995) (397)
The partition of unity finite element method (1996) (393)
Accuracy estimates and adaptive refinements in finite element computations (1986) (388)
Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h - p Version of the FEM (1997) (385)
The finite element method for elliptic equations with discontinuous coefficients (1970) (372)
Survey of meshless and generalized finite element methods: A unified approach (2003) (370)
Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation (2005) (369)
Verification and validation in computational engineering and science: basic concepts (2004) (352)
Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions (1999) (341)
The optimal convergence rate of the p-version of the finite element method (1987) (330)
The post-processing approach in the finite element method—part 1: Calculation of displacements, stresses and other higher derivatives of the displacements (1984) (311)
Stable Generalized Finite Element Method (SGFEM) (2011) (287)
A feedback element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimator (1987) (282)
GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE (2004) (278)
The post‐processing approach in the finite element method—Part 2: The calculation of stress intensity factors (1984) (273)
Finite element-galerkin approximation of the eigenvalues and Eigenvectors of selfadjoint problems (1989) (270)
n-Widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method (2009) (268)
On locking and robustness in the finite element method (1992) (264)
Direct and inverse error estimates for finite elements with mesh refinements (1979) (261)
Validation of A-Posteriori Error Estimators by Numerical Approach (1994) (258)
Locking effects in the finite element approximation of elasticity problems (1992) (257)
Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation (1995) (256)
Nonconforming Elements in the Finite Element Method with Penalty (1973) (251)
The p - and h-p version of the finite element method, an overview (1990) (244)
A discontinuous hp finite element method for diffusion problems: 1-D analysis☆ (1999) (232)
The h , p and h-p versions of the finite element method in 1 dimension. Part II. The error analysis of the h and h-p versions (1986) (227)
On solving elliptic stochastic partial differential equations (2002) (210)
A posteriori error analysis and adaptive processes in the finite element method: Part II—adaptive mesh refinement (1983) (207)
Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems (2010) (205)
Efficient preconditioning for the p -version finite element method in two dimensions (1991) (202)
Analysis of mixed methods using mesh dependent norms (1980) (200)
On the Rates of Convergence of the Finite Element Method (1982) (196)
Theh,p andh-p versions of the finite element method in 1 dimension (1986) (194)
Damage analysis of fiber composites Part I: Statistical analysis on fiber scale (1999) (188)
The generalized finite element method for Helmholtz equation: Theory, computation, and open problems (2006) (184)
The h , p and h-p versions of the finite element methods in 1 dimension . Part III. The adaptive h-p version. (1986) (177)
Error estimates for the combinedh andp versions of the finite element method (1981) (171)
The Post-Processing Approach in the Finite Element Method. Part 3. A Posteriori Error Estimates and Adaptive Mesh Selection. (1984) (170)
Regularity of the solution of elliptic problems with piecewise analytic data. Part 1. Boundary value problems for linear elliptic equation of second order (1988) (169)
The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries (1988) (165)
Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle (1995) (162)
Research directions in computational mechanics (2003) (160)
A model study of the quality of a posteriori error estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles (1994) (158)
Adaptive approaches and reliability estimations in finite element analysis (1979) (155)
Approximation properties of the h-p version of the finite element method (1996) (152)
Introduction to Finite Element Analysis: Formulation, Verification and Validation (2011) (147)
Numerical processes in differential equations (1968) (146)
Solution of Interface Problems by Homogenization. I (1976) (140)
The h, p and h-p version of the finite element method: basis theory and applications (1992) (138)
Analysis of Optimal Finite Element Meshes in R1 (1979) (130)
A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method (1995) (130)
On a dimensional reduction method. I. The optimal selection of basis functions (1981) (129)
The Problem of Selecting the Shape Functions for a p-Type Finite Element (1989) (124)
Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems. Interim report (1975) (123)
A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics (2013) (122)
A Posteriori Error Analysis of Finite Element Solutions for One-Dimensional Problems (1981) (121)
Homogenization Approach In Engineering (1976) (119)
Benchmark computation and performance evaluation for a rhombic plate bending problem (1989) (112)
Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids (2003) (112)
Reliable error estimation and mesh adaptation for the finite element method (1979) (108)
Can a finite element method perform arbitrarily badly? (2000) (106)
A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems (1998) (102)
Geometrically nonlinear analysis of layerwise anisotropic shell structures by hybrid strain based lower order elements (1987) (101)
Finite Element Solution to the Helmholtz Equation with High Wave Number Part II : The hp-version of the FEM (100)
The finite element method for parabolic equations (1982) (98)
The p and h-p Versions of the Finite Element Method; State of the Art. (1986) (97)
Computer‐based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplace's, Poisson's, and the elasticity equations (1996) (97)
Hierarchical Finite Element Approaches Error Estimates and Adaptive Refinement (1981) (94)
Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces. Part I: Approximability of Functions in the Weighted Besov Spaces (2001) (93)
Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements (1992) (93)
Hierarchic models for laminated composites (1992) (92)
Generalized p-FEM in homogenization (2000) (92)
Finite Elements: An Introduction to the Method and Error Estimation (2010) (91)
Lectures on mathematical foundations of the finite element method. (1972) (90)
A posteriori error estimation for finite element solutions of Helmholtz' equation—Part II: estimation of the pollution error (1997) (89)
A Residual-Based A Posteriori Error Estimator for the Stokes-Darcy Coupled Problem (2010) (89)
A systematic approach to model validation based on Bayesian updates and prediction related rejection criteria (2008) (88)
Continuous dependence of eigenvalues on the domain (1965) (88)
Computation of the amplitude of stress singular terms for cracks and reentrant corners (1988) (88)
Meshless and Generalized Finite Element Methods: A Survey of Some Major Results (2003) (86)
The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities (1993) (86)
The problem of plate modeling: theoretical and computational results (1992) (86)
Modeling, mesh generation, and adaptive numerical methods for partial differential equations (1995) (85)
A finite element scheme for domains with corners (1972) (84)
A posteriori error estimation for finite element solutions of Helmholtz’ equation. part I: the quality of local indicators and estimators (1997) (84)
An expert system for the optimal mesh design in the hp‐version of the finite element method (1987) (83)
Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Reaction-Diffusion Problems (1999) (83)
The p‐version of the finite element method for domains with corners and for infinite domains (1990) (83)
A-Posteriori Error Estimates and Adaptive Techniques for the Finite Element Method. (1981) (82)
A posteriori error estimation for generalized finite element methods (2006) (80)
Pollution Error in the h-Version of the Finite Element Method and the Local Quality of the Recovered Derivatives. (1997) (79)
Finite element method for domains with corners (1970) (79)
Locking effects in the finite element approximation of plate models (1995) (78)
Approximation with harmonic and generalized harmonic polynomials in the partition of unity method (1997) (77)
Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty (2005) (76)
The problem of the selection of an a posteriori error indicator based on smoothening techniques (1993) (74)
Effect of numerical integration on meshless methods (2009) (72)
SOLVING STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS BASED ON THE EXPERIMENTAL DATA (2003) (72)
Pollution-error in the h -version of the finite-element method and the local quality of a-posteriori error estimators (1994) (71)
The optimal symmetrical points for polynomial interpolation of real functions in the tetrahedron (1995) (69)
The plate paradox for hard and soft support (1990) (68)
Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ3, Part I: countably normed spaces on polyhedral domains (1997) (68)
The generalized finite element method for Helmholtz equation. Part II: Effect of choice of handbook functions, error due to absorbing boundary conditions and its assessment (2008) (67)
A posteriori error estimation for hierarchic models of elliptic boundary value problems on thin domains (1996) (66)
Regularity of the solution of elliptic problems with piecewise analytic data, II: the trace spaces and application to the boundary value problems with nonhomogeneous boundary conditions (1989) (66)
Hierarchic modeling of plates (1991) (63)
On a dimensional reduction method. II. Some approximation-theoretic results (1981) (63)
A posteriori estimation and adaptive control of the error in the quantity of interest. Part I: A posteriori estimation of the error in the von Mises stress and the stress intensity factor (2000) (63)
p Interpolation Error Estimates for Edge Finite Elements of Variable Order in Two Dimensions (2003) (62)
On the mixed finite element method with Lagrange multipliers (2003) (62)
Computational error estimates and adaptive processes for some nonlinear structural problems (1982) (62)
On principles for the selection of shape functions for the Generalized Finite Element Method (2002) (61)
Reliable stress and fracture mechanics analysis of complex components using a h–p version of FEM (1995) (61)
The finite element method for parabolic equations (1982) (61)
Reliability of infinite element methods for the numerical computation of waves (1997) (60)
The Babuška-Brezzi condition and the patch test: an example (1997) (59)
On the exponential convergence of the h-p version for boundary element Galerkin methods on polygons (1990) (59)
Estimates for the errors in Eigenvalue and Eigenvector approximation by Galerkinmethods, with particular attention to the case of multiple Eigenvalues (1987) (59)
p‐version of the generalized FEM using mesh‐based handbooks with applications to multiscale problems (2004) (58)
A MODEL STUDY OF THE QUALITY OF A POSTERIORI ERROR ESTIMATORS FOR FINITE ELEMENT SOLUTIONS OF LINEAR ELLIPTIC PROBLEMS, WITH PARTICULAR REFERENCE TO THE BEHAVIOR NEAR THE BOUNDARY (1997) (58)
A POSTERIORI ERROR ESTIMATION FOR THE FINITE ELEMENT METHOD-OF-LINES SOLUTION OF PARABOLIC PROBLEMS (1999) (55)
Optimal estimates for lower and upper bounds of approximation errors in the p-version of the finite element method in two dimensions (2000) (54)
Reliability of computational science (2007) (53)
Analysis of finite element methods for second order boundary value problems using mesh dependent norms (1980) (53)
An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type (1986) (53)
Higher order stable generalized finite element method (2014) (53)
A numerical method with a posteriori error estimation for determining the path taken by a propagating crack (1998) (52)
Quadrature for meshless methods (2008) (52)
Approximation by Hill functions. II. (1970) (52)
Bayesian inference and model comparison for metallic fatigue data (2015) (52)
Strongly stable generalized finite element method: Application to interface problems (2017) (51)
On a dimensional reduction method. III. A posteriori error estimation and an adaptive approach (1981) (50)
A Global-Local Approach for the Construction of Enrichment Functions for the Generalized FEM and Its Application to Three-Dimensional Cracks (2007) (50)
Beams, Plates and Shells (2011) (49)
Adaptive Methods and Error Estimation for Elliptic Problems of Structural Mechanics. (1983) (49)
On the Stability of the Discontinuous Galerkin Method for the Heat Equation (1997) (49)
Basic principles of feedback and adaptive approaches in the finite element method (1986) (47)
THE PLATE PARADOX FOR HARD AND SOFT SIMPLE SUPPORT by (46)
Worst case scenario analysis for elliptic problems with uncertainty (2005) (45)
The Rate of Convergence for the Finite Element Method (1971) (45)
Finite element method for solving problems with singular solutions (1996) (43)
Effects of uncertainties in the domain on the solution of Neumann boundary value problems in two spatial dimensions (2002) (43)
Validation Challenge Workshop (2008) (42)
Analysis of optimal finite-element meshes in ¹ (1979) (42)
Robustness in stable generalized finite element methods (SGFEM) applied to Poisson problems with crack singularities (2016) (40)
Regularity and numerical solution of eigenvalue problems with piecewise analytic data (1989) (39)
An approach for constructing families of homogenized equations for periodic media. I: an integral representation and its consequences (1991) (39)
The p -version of the finite element method for the elliptic boundary value problems with interfaces (1992) (39)
Guaranteed computable bounds for the exact error in the finite element solution. Part I : One-dimensional model problem (1999) (39)
Mixed-hybrid finite element approximations of second-order elliptic boundary value problems. Part 2 - weak-hybrid methods (1978) (38)
Numerical treatment of eigenvalue problems for differential equations with discontinuous coefficients. [''Factoring'' procedure] (1977) (38)
Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ3. Part II: Regularity in neighbourhoods of edges (1997) (38)
Predictive Computational Science: Computer Predictions in the Presence of Uncertainty (2017) (38)
On the reliability and optimality of the finite element method (1979) (37)
On one approach to a posteriori error estimates for evolution problems solved by the method of lines (2001) (37)
Numerical treatment of vertex singularities and intensity factors for mixed boundary value problems for the Laplace equation in R 3 (1994) (37)
Finite Element Methods for the Solution of Problems with Rough Input Data. (1985) (36)
Generalized finite element method for second-order elliptic operators with Dirichlet boundary conditions (2008) (36)
A posteriori error estimation for the semidiscrete finite element method of parabolic differential equations (2001) (36)
Mesh‐independent p‐orthotropic enrichment using the generalized finite element method (2002) (34)
Solution of Problems with Interfaces and Singularities (1974) (34)
The partition of unity method for the elastically supported beam (1998) (34)
A numerical procedure for the determination of certain quantities related to the stress intensity factors in two-dimensional elasticity (1995) (33)
Some aspects of parallel implementation of the finite-element method on message passing architectures (1989) (33)
Stress computations for nearly incompressible materials by the p‐version of the finite element method (1989) (33)
On the posteriori estimation of the modeling error for the heat conduction in a plate and its use for adaptive hierarchical modeling (1994) (33)
Numerical stability in mathematical analysis (1968) (32)
An Error Analysis for the Finite Element Method Applied to Convection Diffusion Problems. (1982) (30)
The Splitting Method as a Tool for Multiple Damage Analysis (2005) (30)
On the Regularity of Elasticity Problems with Piecewise Analytic Data (1993) (30)
The treatment of nonhomogeneous Dirichlet boundary conditions by thep-version of the finite element method (1989) (29)
Guaranteed computable bounds for the exact error in the finite element solution—Part II: bounds for the energy norm of the error in two dimensions† (2000) (29)
An expert-system-like feedback approach in the hp -version of the finite element method (1987) (29)
Superconvergence in the generalized finite element method (2007) (29)
Strongly Stable Generalized Finite Element Method (SSGFEM) for a non-smooth interface problem (2019) (29)
DIRECT AND INVERSE APPROXIMATION THEOREMS FOR THE p-VERSION OF THE FINITE ELEMENT METHOD IN THE FRAMEWORK OF WEIGHTED BESOV SPACES PART II: OPTIMAL RATE OF CONVERGENCE OF THE p-VERSION FINITE ELEMENT SOLUTIONS (2002) (29)
Dynamic data‐driven finite element models for laser treatment of cancer (2007) (29)
Theh, p andh-p versions of the finite element method in 1 dimension (1986) (29)
Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems (2003) (28)
Machine Computation Using the Exponentially Convergent Multiscale Spectral Generalized Finite Element Method (2014) (28)
Finite Element Methods: Principles for Their Selection. (1984) (28)
On the approximability and the selection of particle shape functions (2004) (27)
Assessment of the cost and accuracy of the generalized FEM (2007) (27)
Parallel Implementation of the hp-Version of the Finite Element Method on a Shared-Memory Architecture (1990) (26)
Theh, p andh-p versions of the finite element method in 1 dimension (1986) (26)
The h-p version of the boundary element method with geometric mesh on polygonal domains (1990) (25)
Mathematical Modeling and Numerical Simulation in Continuum Mechanics (2001) (25)
HOMOGENIZATION OF MATERIALS WITH PERIODIC TRUSS OR FRAME MICRO-STRUCTURES (2007) (24)
A Survey of a Posteriori Error Estimators and Adaptive Approaches in the Finite Element Method. (1982) (24)
Mechanics of Materials with Periodic Truss or Frame Micro-Structures (2007) (24)
A model study of element residual estimators for linear elliptic problems : the quality of the estimators in the interior of meshes of triangles and quadrilaterals (1995) (24)
A stable generalized finite element method (SGFEM) of degree two for interface problems (2020) (23)
Basic problems of a posteriori error estimation (1992) (23)
Development of a Computational Paradigm for Laser Treatment of Cancer (2006) (23)
The problem of modeling the elastomechanics in engineering (1990) (22)
Practical aspects of a-posteriori estimation for reliable finite element analysis 1 Dedicated to Pro (1998) (22)
Solution of Helmholtz problems by knowledge-based FEM (1997) (22)
Pollution problem of the p‐ and h–p versions of the finite element method (1987) (21)
ANALYSIS AND FINITE ELEMENT METHODS FOR A FLUID-SOLID INTERACTION PROBLEM IN ONE DIMENSION (1996) (21)
Courant Element: Before and After (1994) (21)
The finite element method for infinite domains. I (1972) (21)
Reliability Of Finite Element Methods For TheNumerical Computation Of Waves (1970) (20)
Multiscale-Spectral GFEM and Optimal Oversampling (2019) (20)
L2-GLOBAL TO LOCAL PROJECTION: AN APPROACH TO MULTISCALE ANALYSIS (2011) (19)
hp Optimization of finite element approximations: Analysis of the optimal mesh sequences in one dimension (1997) (19)
e%-superconvergence in the interior of locally refined meshes of quadrilaterals: superconvergence of the gradient in finite element solutions of Laplace's and Poisson's equations (1994) (19)
A note on conjugate gradient convergence (1997) (19)
Mesh-independent directional p-enrichment using the generalized finite element method (2001) (19)
Some applications of the discrete fourier transform to problems of crystal lattice deformation I (1960) (19)
Interior numerical approximation of boundary value problems with a distributional data (2004) (19)
Performance of the h–p version of the finite element method with various elements (1993) (19)
The penetration function and its application to microscale problems (2008) (19)
Corrigendum: “Finite element-Galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems” [Math. Comp. 52 (1989), no. 186, 275–297; MR0962210 (89k:65132)] (1994) (18)
Dealing with uncertainties in engineering problems using only available data (2014) (18)
Quality assessment of the a-posteriori error estimation in finite elements (1992) (18)
η%-Superconvergence of finite element approximations in the interior of general meshes of triangles (1995) (17)
Acta Numerica 2003: Survey of meshless and generalized finite element methods: A unified approach (2003) (17)
Performance of the h, p and h-p versions (1984) (16)
A Convergence Analysis of an H-Version Finite-Element Method with High-Order Elements for Two-Dimensional Elasto-Plasticity Problems (1997) (16)
The problem of verification with reference to the Girkmann problem (2010) (16)
A continuous analogue of sturm sequences in the context of Sturm-Liouville equation (1989) (16)
A stochastic multiscale method for the elastodynamic wave equation arising from fiber composites (2014) (15)
Dispersion Analysis and Error Estimation of Galerkin Finite Element Methods for the Numerical Computation of Waves (1994) (15)
Dimensional reduction for nonlinear boundary value problems (1988) (15)
On solving stochastic initial-value differential equations (2003) (15)
Computational Aspects of the Finite Element Method (1977) (15)
A posteriori estimation of the error in the recovered derivatives of the finite element solution (1997) (15)
A convergence analysis of a P-version finite element method for one-dimensional elastoplasticity problem with constitutive laws based on the gauge function method (1996) (14)
Computational aspects of the determination of the stress intensity factors for two-dimensional elasticity (1989) (14)
A global-local approach for the construction of enrichment functions for the generalized FEM and its application to propagating three-dimensional cracks (2006) (14)
Optimal Shear Correction Factors in Hierarchical Plte Modelling (1991) (14)
Analysis and computation of a cyclic plasticity model by aid of Ddassl (1997) (14)
Formulation of the static frame problem (2008) (13)
Break-off model for CaCO3 fouling in heat exchangers (2018) (13)
Finite element analysis of the Girkmann problem using the modern hp-version and the classical h-version (2012) (13)
Adaptive Finite Element Processes in Structural Mechanics. (1984) (13)
Mathematical problems of computational decisions in the finite element method. Technical report TR-426 (1975) (12)
An Enriched Immersed Finite Element Method for Interface Problems with Nonhomogeneous Jump Conditions (2020) (12)
On randomised solutions of Laplace's equation (1961) (12)
Nonuniform Error Estimates for the Finite Element Method (1975) (12)
Direct and inverse approximation theorems for the pp-version of the finite element method in the framework of weighted Besov spaces, part III: Inverse approximation theorems (2013) (12)
Implementation of nonhomogeneous dirichlet boundary conditions in the p version of the finite element method (1989) (12)
Guaranteed a posteriori error estimation for fully discrete solutions of parabolic problems (2003) (12)
Computational Aspects of the h, p and h-p Versions of the Finite Element Method. (1987) (11)
Feedback, Adaptivity and A-Posterior Estimates in Finite Elements: Aims, Theory and Experience. (1984) (11)
Quantitative Assessment of the Accuracy of Constitutive Laws for Plasticity with an Emphasis on Cyclic Deformation (1993) (11)
THE FINITE ELEMENT METHOD FOR ELLIPTIC DIFFERENTIAL EQUATIONS (1971) (11)
Advances in the p and h-p Versions of the Finite Element Method. A Survey (1988) (11)
Some aspects of parallel implementation of the finite-element method on message passing architectures* * (1990) (11)
Boundary value problems in spaces of distributions on smooth and polygonal domains (2008) (11)
Self-adaptive refinements in the finite element method (1975) (11)
The computational aspects of the homogenization problem (1979) (11)
A priori error estimates of finite element solutions of parametrized strongly nonlinear boundary value problems (1997) (11)
On Roundoff Error Growth in Elliptic Problems (2018) (10)
Local Jacobi Operators and Applications to the p-Version of Finite Element Method in Two Dimensions (2010) (10)
The Factorization Method for the Numerical Solution of Two Point Boundary Value Problems for Linear ODE's (Ordinary Differential Equations). (1987) (10)
The effect of numerical integration on the finite element approximation of linear functionals (2011) (10)
Pointwise error estimate of the Legendre expansion: The known and unknown features (2019) (10)
A-posteriori Error Estimation for the Finite Element Method (1981) (10)
Composites with a Periodic Structure, Mathematical Analysis and Numerical Treatment. (1985) (10)
Algebraic algorithms for the analysis of mechanical trusses (2004) (10)
Information-based numerical practice (1987) (9)
Validation Challenge Workshop Summary. (2008) (9)
The Theory and Practice of the h-p Version of Finite Element Method. (1987) (9)
The p-Version of the Finite Element Method for Constraint Boundary Conditions. (1988) (9)
A Numerical Method for Steady State Free Boundary Problems (1996) (9)
The asymptotically optimal meshsize function for bi-p degree interpolation over rectangular elements (1998) (8)
Using Cyber-Infrastructure for Dynamic Data Driven Laser Treatment of Cancer (2007) (8)
Uncertainties in Engineering Design. Mathematical Theory and Numerical Experience. (1986) (8)
A fuzzy-stochastic multiscale model for fiber composites: A one-dimensional study (2015) (8)
Accuracy of some plate models for clamped-in boundary conditions (1992) (8)
Spatial Poisson processes for fatigue crack initiation (2018) (8)
A Posteriori Error Estimates of Finite Element Solutions of Parametrized Nonlinear Equations (1992) (8)
Trends in finite elements (1989) (7)
THE THEORY OF DENSITY REPRESENTATION OF FINITE ELEMENT MESHES. EXAMPLES OF DENSITY OPERATORS WITH QUADRILATERAL ELEMENTS IN THE MAPPED DOMAIN (1993) (7)
A-posteriori estimation of the error in the error estimate (1998) (7)
A remark to the finite element method (1971) (7)
The Postprocessing Technique in the Finite Element Method - The Theory and Experience. (1984) (7)
The computational modeling of problems on domains with small holes (2017) (7)
Stress Computations for Nearly Incompressible Materials (1988) (7)
Strongly Stable Generalized Finite Element Method (SSGFEM) for a non-smooth interface problem II: A simplified algorithm (2020) (6)
Mathematical and computational problems in reactor calculations (1973) (6)
Some applications of the discrete fourier transform to problems of crystal lattice deformation II (1960) (6)
The dome and the ring: Verification of an old mathematical model for the design of a stiffened shell roof (2012) (6)
Static frame challenge problem : Summary (2008) (6)
THE CONNECTION BETWEEN THE FINITE DIFFERENCE LIKE METHODS AND THE METHODS BASED ON INITIAL VALUE PROBLEMS FOR ODE (1975) (6)
Computational aspects and adaptive solution methods in the finite element method for non-linear, parametrized problems (1990) (6)
NEW FICTITIOUS DOMAIN METHODS: FORMULATION AND ANALYSIS (2005) (6)
The boundary layer for p-model plate problems part I. Asymptotic analysis (1997) (6)
Study of Superconvergence by a Computer-Based Approach. Superconvergence of the Gradient in Finite Element Solutions of Laplace's and Poisson's Equations (1993) (6)
Numerical experiments with finite element method I (1970) (5)
Efficient solution of lattice equations by the recovery method Part I: Scalar elliptic problems (2004) (5)
On the generalized plane strain problem in thermoelasticity (2006) (5)
An Asymptotically Exact, Pointwise, a Posteriori Error Estimator for Linear, Elliptic, One Dimensional Problems with Possible Singularities in the Solution (1994) (5)
V&V in Computational Engineering and Science. Part 1: Basic Concepts (2003) (5)
A cut-cell finite element method for Poisson’s equation on arbitrary planar domains (2021) (5)
Dimensional reduction for Helmholtz's equation on a bounded domain (1997) (5)
Efficient Solution of Anisotropic Lattice Equations by the Recovery Method (2008) (5)
Numerical treatment of engineering problems with uncertainties. The fuzzy set approach and its application to the heat exchanger problem (2011) (5)
Approximate and Low Regularity Dirichlet Boundary Conditions in the Generalized Finite Element Method (2007) (5)
A Computational Infrastructure for Reliable Computer Simulations (2003) (4)
Adaptive Hierarchic Modelling of Plates and Shells with A-Posteriori Error Estimation (1992) (4)
Regularity of solutions to a one dimensional plasticity model (1998) (4)
A Posteriori Estimators for the FEM: Analysis of the Robustness of the Estimators for the Poisson Equation (2001) (4)
A posteriori error analysis and adaptive processus in the finite element method. I: Error analysis (1983) (4)
Interior maximum norm estimates for finite element discretizations of the Stokes equations (2007) (4)
On A System For Adaptive, Parallel Finite Element Computations (1978) (4)
Appendix A: Definitions (2011) (4)
Adaptive procedure for approximating functions by continuous piecewise polynomials (1996) (4)
Olek and a Mathematician (1991) (3)
Multilevel Preconditioning Methods for Discrete Models of Lattice Block Materials (2008) (3)
The boundary layer for p-model plate problems part II. Boundary layer behavior (1997) (3)
An anisotropic sparse grid stochastic collocation method for PDEs with random input data. (2007) (3)
Reliability of Computational Analysis of Plasticity Problems (1991) (3)
Study of Superconvergence by a Computer-Based Approach: Superconvergence of the Gradient of the Displacement, The Strain and Stress in Finite Element Solutions for Plane Elasticity. (1994) (3)
Introduction to Finite Element Analysis (1990) (3)
Computation of derivatives in the finite element method (1970) (3)
Lectures on the Numerical Solution of Partial Differential Equations. (1981) (3)
A condensed generalized finite element method (CGFEM) for interface problems (2022) (3)
Problems of Optimization and Numerical Stability in Computations (2010) (3)
On Schwarz' algorithms in partial differential equations of mathematical physics (1958) (2)
Superconvergence of elliptic reconstructions of finite element solutions of parabolic problems in domains with piecewise smooth boundaries (2012) (2)
Locking Effects for the Reissner-Mindlin Plate Model (1992) (2)
Chapter 4 The Postprocessing Technique in the Finite Element Method. The Theory & Experience (1984) (2)
MATHEMATICAL FRAMEWORK FOR LATTICE PROBLEMS (2007) (2)
Stable generalized finite element method (SGFEM) for three-dimensional crack problems (2022) (2)
A simpler way to handle complex analysis (1998) (2)
What Do We Want and What Do We Have in a Posteriori Estimates in the FEM (2000) (2)
Polynomial Interpolation of Real Functions 1: Interpolation in an Interval (1993) (2)
A Dynamic Data Driven Computational Infrastructure for Reliable Computer Simulations (2004) (2)
Selection of Finite Element Methods. (1981) (2)
The Factorization Method for Two Points Boundary Value Problems for ODE's and Its Relation to the Finite Difference Method. (1984) (2)
Accuracy of the Reissner-Mindlin and the (1,1,2) Model for the Clamped-in Plate Problem (1990) (2)
Robustness of error estimators for finite element solutions of problems with high orthotropy (2009) (2)
Finite element analysis of the Girkmann problem using the modern hp-version and the (2010) (1)
Comments on the Development of Computational Mathematics in Czechoslovakia and in the USSR. (1987) (1)
Problem of selecting the shape functions for a p-type finite element. Final report (1988) (1)
Solution Of Stochastic Partial Differential Equations ( SPDEs ) Using Galerkin Method And Finite Element Techniques (2006) (1)
Selections of shape functions for dimensional reduction to Helmholtz's equation (1999) (1)
Can We Trust the Computational Analysis of Engineering Problems (2002) (1)
η%-Superconvergence of Finite Element Solutions and Error Estimators (2001) (1)
Comments on postwar development of computational mathematics in some countries of Eastern Europe (1987) (1)
Recent progress in the p and h-p version of the finite element method (1989) (1)
Computational Mechanics: Where Is It Going? (2001) (1)
Chapter I - Reality, Mathematics, and Computation (2004) (1)
Interval arithmetic error estimation for the solution of Fredholm integral equation (2009) (1)
Benchmark Computation and Finite Element Performance Evaluation for a Rhombic Plate Bending Problem (1987) (1)
The non-linear theory of internal friction (1959) (1)
A-posteriori error estimates for the finite element method. Technical report TR-581 (1977) (1)
Finite Element Spaces (2011) (1)
Are High Degree Elements Preferable? Some Aspects of the h and h-p Version of the Finite Element Method (1987) (1)
p-version of the finite-element method. [COMET X] (1979) (1)
The development of computational mathematics in Czechoslovakia and the USSR (1990) (1)
Stochastic differential equations (1959) (0)
A posteriori estimation of the error in the error estimate (1999) (0)
Polynomial Interpolation and Approximation of Real Functions 2: Symmetrical Interpolation for the Triangle (1993) (0)
Appendix D: Computation of Stress Intensity Factors (2011) (0)
Regularity and Rates of Convergence (2011) (0)
What I know and would like to know about The Meshless and Generalized FEM (0)
Applications of Mathematics (2015) (0)
What Should be Computed and why (2011) (0)
Essentials of Sensitivity and Functional Analysis (2004) (0)
Methodology of model development in the applied sciences (2021) (0)
Chapter VII – Contact Problems in Elasticity and Thermoelasticity (2004) (0)
RELIABILITY ESTIMATES AND ADAPTIVITY IN FINITE ELEMENT ENGINEERNG COMPUTATIONS. (1982) (0)
Appendix F: Solutions for Selected Exercises (2011) (0)
Jindřich Nečas in the Early 1960s (2015) (0)
On the Patch Type Finite Element Method (1995) (0)
In memory of Prof. František Vyčichlo (1958) (0)
Don't believe everything you calculate from a handbook (1998) (0)
Optimal regularization of summation methods of a Fourier series (1966) (0)
Computation and Verification of Data (2011) (0)
Approximate Dirichlet boundary conditions in the generalized finite element method (2006) (0)
Numerical Solution of Problems of Cyclic Plasticity (1999) (0)
Appendix C: Properties of the Stress Tensor (2011) (0)
Numerical stability of the Ritz method (1965) (0)
Numerical Solution of Partial Differential Equations (1974) (0)
Final Report on the Special Year in Numerical Analysis, 1980-81. (1981) (0)
Mathematical modeling and numerical simulation in continuum mechanics : proceedings of the international symposium on mathematical modeling and numerical simulation in continuum mechanics, September 29 - October 3, 2000 Yamaguchi, Japan (2002) (0)
On the optimal computation of Fourier coefficients (1966) (0)
Reliability of Computer Predictions In Computational Solid Mechanics : Towards the Estimation and Control of Errors Due to Modeling , Discretization , and Uncertainty (2006) (0)
The Reliability Estimates and Adaptivity in Finite Element Engineering Computations (1982) (0)
Chapter II - General Abstract Scheme and the Analysis of the Worst Scenario Method (2004) (0)
An Analysis of a Finite Element Method for Convection-Diffusion Problems. Part I. Quasi-Optimality. (1983) (0)
A generalized method for the dispersion analysis of finite element solutions for the Helmholtz equation (1999) (0)
Problem of stability of solutions of elliptic differential equations (with respect to small changes of regions of definition) [Lecture] (1958) (0)
Multiscale Bayesian model for uncertainty quantification in porous media (2014) (0)
An Introduction to the FEARS (Finite Element Adaptive Research Solver) Program (1983) (0)
Formulation of Mathematical Models (2011) (0)
NASTRAN and FEARS Analyses of Two Problems of Plane Elasticity. (1982) (0)
ICES REPORT #04-06 A COMPUTATIONAL INFRASTRUCTURE FOR RELIABLE COMPUTER SIMULATIONS (2004) (0)
Chapter IX - Flow Theories of Plasticity (2004) (0)
An Analysis of a Finite Element Method for Convection-Diffusion Problems. Part II. A Posteriori Error Estimates and Adaptivity. (1983) (0)
Appendix B: Numerical Quadrature (2011) (0)
Chapter V - Elastic and Thermoelastic Beams (2004) (0)
Guaranteed a-posteriori error estimation for semi-discrete solutions of parabolic problems based on elliptic reconstruction (2022) (0)
Feasibility of Applying the Finite Element Adaptive Research Solver (FEARS) Program to the Plate Bending Problem. (1983) (0)
On regularization of the optimal formula for computing Fourier coefficients (1967) (0)
An Outline of the Finite Element Method (2011) (0)
Fifty Years of Applications of Mathematics (2006) (0)
ALGEBRAIC ALGORITHMS FOR THE ANALYSIS OF MECHANICAL (2004) (0)
Higher order stable generalized finite element method (2014) (0)
Subspace Correction Methods for the Iterative Solution of Hierarchic Plate Models. 1: Heat Transfer Problems (1994) (0)
Finite element analysis of the Girkmann problem using the modern hp-version and the classical h-version (2011) (0)
Appendix E: Saint‐Venant's principle (2011) (0)

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