Philippe G. Ciarlet

Philippe G. Ciarlet's AcademicInfluence.com Rankings

Philippe G. Ciarlet

Mathematics

#1856

World Rank

#2952

Historical Rank

Applied Mathematics

#66

World Rank

#78

Historical Rank

Measure Theory

#341

World Rank

#512

Historical Rank

mathematics Degrees

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Mathematics

Why Is Philippe G. Ciarlet Influential?

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According to Wikipedia, Philippe G. Ciarlet is a French mathematician, known particularly for his work on mathematical analysis of the finite element method. He has contributed also to elasticity, to the theory of plates and shells and differential geometry.

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Philippe G. Ciarlet's Published Works

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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 finite element method for elliptic problems (2002) (9784)
Basic error estimates for elliptic problems (1991) (1170)
Mathematical elasticity, volume I: Three-dimensional elasticity (1989) (801)
Three-dimensional elasticity (1988) (532)
Maximum principle and uniform convergence for the finite element method (1973) (494)
Linear and Nonlinear Functional Analysis with Applications (2013) (473)
General lagrange and hermite interpolation in Rn with applications to finite element methods (1972) (470)
An Introduction to Differential Geometry with Applications to Elasticity (2006) (446)
Introduction to Numerical Linear Algebra and Optimisation (1989) (399)
Introduction a l'analyse numerique matricielle et a l'optimisation (1984) (393)
JUSTIFICATION OF THE TWO-DIMENSIONAL LINEAR PLATE MODEL. (1979) (359)
Mathematical elasticity. volume II, Theory of plates (1997) (337)
The Finite Element Method for Elliptic Problems. (1981) (270)
A justification of the von Kármán equations (1980) (255)
Interpolation theory over curved elements, with applications to finite element methods (1972) (251)
Plates and Junctions in Elastic Multi-Structures: An Asymptotic Analysis (1991) (221)
Discrete maximum principle for finite-difference operators (1970) (216)
THE COMBINED EFFECT OF CURVED BOUNDARIES AND NUMERICAL INTEGRATION IN ISOPARAMETRIC FINITE ELEMENT METHODS (1972) (211)
A Justi cation of a Nolinear Model in Plate Theory (1979) (196)
Theory of plates (1997) (162)
A Mixed Finite Element Method for the Biharmonic Equation (1974) (160)
Plates And Junctions In Elastic Multi-Structures (1990) (142)
Existence theorems for two-dimensional linear shell theories (1994) (136)
Asymptotic analysis of linearly elastic shells. II. Justification of flexural shell equations (1996) (117)
Numerical analysis of the finite element method (1976) (116)
Theory of Shells (2000) (112)
ANOTHER APPROACH TO LINEARIZED ELASTICITY AND A NEW PROOF OF KORN'S INEQUALITY (2005) (110)
Junctions between three-dimensional and two-dimensional linearly elastic structures (1989) (106)
Introduction to Linear Shell Theory (1989) (104)
Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations (1996) (100)
Two-dimensional approximations of three-dimensional eigenvalue problems in plate theory (1981) (99)
Numerical Methods for Fluids, Part 3 (2003) (92)
Asymptotic analysis of linearly elastic shells. III. Justification of Koiter's shell equations (1996) (91)
A justification of the Marguerre-von Kármán equations (1986) (83)
Numerical methods for fluids (2003) (79)
Asymptotic analysis of linearly elastic shells: ‘Generalized membrane shells’ (1996) (71)
Unilateral problems in nonlinear, three-dimensional elasticity (1985) (71)
On the characterizations of matrix fields as linearized strain tensor fields (2006) (70)
ON THE NEWTON–KANTOROVICH THEOREM (2012) (70)
On the ellipticity of linear membrane shell equations (1996) (68)
Handbook of Numerical Analysis (1976) (64)
Justification of the two-dimensional equations of a linearly elastic shallow shell (1992) (63)
Multipoint Taylor formulas and applications to the finite element method (1971) (63)
Numerical methods of high-order accuracy for singular nonlinear boundary value problems (1970) (62)
On the recovery of a surface with prescribed first and second fundamental forms (2002) (54)
Dual iterative techniques for solving a finite element approximation of the biharmonic equation (1975) (45)
An existence and uniqueness theorem for the two-dimensional linear membrane shell equations (1996) (44)
A NEW DUALITY APPROACH TO ELASTICITY (2012) (41)
Recovery of a Manifold with Boundary and its Continuity as a Function of its Metric Tensor (2004) (39)
Finite element methods (1991) (38)
Two- and three-field formulations for wave transmission between media with opposite sign dielectric constants (2007) (38)
Interpolation error estimates for the reduced Hsieh-Clough-Tocher triangle (1978) (37)
On Korn’s inequality (2010) (36)
Intrinsic methods in elasticity: a mathematical survey (2008) (35)
JUSTIFICATION OF A TWO-DIMENSIONAL NONLINEAR SHELL MODEL OF KOITER＇S TYPE (2001) (34)
Lectures on Three-Dimensional Elasticity (1983) (33)
On a lemma of Jacques-Louis Lions and its relation to other fundamental results (2015) (33)
Continuity of a Deformation as a Function of its Cauchy-Green Tensor (2003) (32)
Discrete variational Green's function (1970) (32)
Continuity of a Deformation in H1 as a Function of Its Cauchy-Green Tensor in L1 (2004) (31)
Conforming and nonconforming finite element methods for solving the plate problem (1974) (30)
Nonlinear Korn inequalities (2015) (30)
Another approach to linear shell theory and a new proof of Korn's inequality on a surface (2005) (29)
Some results in the theory of nonnegative matrices (1968) (29)
Existence theorems in intrinsic nonlinear elasticity (2010) (28)
Trends and applications of pure mathematics to mechanics : invited and contributed papers presented at a symposium at Ecole Polytechnique, Palaiseau, France, November 28-December 2, 1983 (1984) (28)
An Existence Theorem for Nonlinearly Elastic ‘Flexural’ Shells (1998) (28)
ON KORN'S INEQUALITIES IN CURVILINEAR COORDINATES (2001) (28)
Lectures on The Finite Element Method (1975) (27)
Recent Progress in the Two-Dimensional Approximation of Three - Dimensional Plate Models in Nonlinear Elasticity (1987) (27)
The Continuity of a surface as a function of its two fundamental forms (2003) (26)
Modeling and justification of eigenvalue problems for junctions between elastic structures (1989) (25)
On the ellipticity of linear shell models (1992) (25)
Mathematical Modeling and Numerical Simulation in Continuum Mechanics (2001) (25)
On Saint Venant's compatibility conditions and Poincaré's lemma (2006) (24)
Another approach to linearized elasticity and Korn's inequality (2004) (24)
On rigid and infinitesimal rigid displacements in shell theory (2004) (23)
From the classical to the generalized von Kármán and Marguerre-von Kármán equations (2006) (21)
An 0 (h2) method for a non-smooth boundary value problem (1968) (21)
A nonlinear Korn inequality on a surface (2006) (21)
INTRINSIC FORMULATION OF THE DISPLACEMENT- TRACTION PROBLEM IN LINEARIZED ELASTICITY (2014) (20)
An obstacle problem for elliptic membrane shells (2018) (20)
RECOVERY OF A SURFACE WITH BOUNDARY AND ITS CONTINUITY AS A FUNCTION OF ITS TWO FUNDAMENTAL FORMS (2005) (20)
SAINT VENANT COMPATIBILITY EQUATIONS ON A SURFACE APPLICATION TO INTRINSIC SHELL THEORY (2008) (20)
On rigid and infinitesimal rigid displacements in three-dimensional elasticity (2003) (20)
DIRECT COMPUTATION OF STRESSES IN PLANAR LINEARIZED ELASTICITY (2009) (19)
Advances in deterministic and stochastic analysis (2007) (19)
A confinement problem for a linearly elastic Koiter's shell (2019) (18)
Justification of the boundary conditions of a clamped plate by an asymptotic analysis (1989) (17)
Legendre–Fenchel duality in elasticity (2011) (17)
Another approach to the fundamental theorem of riemannian geometry in R3, by way of rotation fields (2007) (16)
Techniques of Scientific Computing (1997) (16)
On the Existence of Solutions to the Generalized Marguerre-von Kármán Equations (2006) (15)
A New Approach to the Fundamental Theorem of Surface Theory (2008) (15)
A remark on the von kármán equations (1983) (15)
A NEW APPROACH TO LINEAR SHELL THEORY (2005) (15)
ORDERS OF CONVERGENCE IN FINITE ELEMENT METHODS (1973) (14)
An Introduction to Shell Theory (2008) (14)
Techniques of scientific computing (Part 2) (1997) (14)
A Poincaré inequality in a Sobolev space with a variable exponent (2011) (13)
Nonlinear Korn inequalities in Rn and immersions in W2,p, p > n, considered as functions of their metric tensors in W1,p (2016) (13)
Mathematical modelling of linearly elastic shells (2001) (13)
Mathematical Elasticity: Theory of Plates (2021) (12)
New nonlinear estimates for surfaces in terms of their fundamental forms (2017) (12)
An obstacle problem for Koiter’s shells (2019) (12)
Existence Theorem for a Nonlinear Elliptic Shell Model (2015) (12)
NONLINEAR SAINT–VENANT COMPATIBILITY CONDITIONS AND THE INTRINSIC APPROACH FOR NONLINEARLY ELASTIC PLATES (2013) (12)
On the convergence of the semi-discrete incremental method in nonlinear, three-dimensional, elasticity (1984) (11)
An estimate of the H1-norm of deformations in terms of the L1-norm of their Cauchy–Green tensors (2004) (10)
Finite difference methods (part 1) ; Solution of equations in R[n] (part 1) (1990) (10)
An Existence Theorem for Generalized von Kármán Equations (2001) (10)
On Korn's inequalities on a surface (2016) (10)
A mathematical model of Koiter’s type for a nonlinearly elastic “almost spherical” shell (2016) (9)
LAGRANGE MULTIPLIERS IN INTRINSIC ELASTICITY (2011) (9)
SAINT VENANT COMPATIBILITY EQUATIONS IN CURVILINEAR COORDINATES (2007) (9)
Mathematical Elasticity: Theory of Shells (2021) (9)
Finite element methods (part 2) . Numerical methods for solids (part 2) (1996) (9)
Discrete variational Green's function. I (1969) (9)
An existence theorem for a two-dimensional nonlinear shell model of Koiter’s type (2018) (9)
Orientation-preserving condition and polyconvexity on a surface: Application to nonlinear shell theory (2013) (9)
Differential Geometry: Theory and Applications (2008) (8)
Discrete maximum principle for finite-difference operators (1970) (8)
The pure displacement problem in nonlinear three-dimensional elasticity: intrinsic formulation and existence theorems (2009) (8)
Essential Computational Modeling in Chemistry : A derivative of Handbook of Numerical Analysis Special Volume : Computational Chemistry, Vol 10 (2011) (8)
CESÀRO–VOLTERRA PATH INTEGRAL FORMULA ON A SURFACE (2009) (8)
Computational chemistry : special volume (2003) (7)
A Two-Dimensional Non-Linear Shell Model of Koiter’s Type (2003) (7)
ON THE GENERALIZED VON KÁRMÁN EQUATIONS AND THEIR APPROXIMATION (2007) (7)
6. Finite Element Methods for the Plate Problem (2002) (7)
Boundary conditions in intrinsic nonlinear elasticity (2014) (7)
FRÉCHET DIFFERENTIABILITY OF THE NORM IN A SOBOLEV SPACE WITH A VARIABLE EXPONENT (2013) (7)
A Cesàro-Volterra formula with little regularity (2010) (7)
Korn's inequalities: The linear vs. the nonlinear case (2011) (6)
A notion of polyconvex function on a surface suggested by nonlinear shell theory (2011) (6)
A new class of variational problems arising in the modeling of elastic multi-structures (1990) (6)
Ellipticity of bending and membrane shell equations (1995) (6)
A new approach for approximating linear elasticity problems (2008) (6)
Justification of the Darboux–Vallée–Fortuné compatibility relation in the theory of surfaces (2008) (6)
Donati compatibility conditions for membrane and flexural shells (2015) (6)
Remarks on a lemma by Jacques-Louis Lions (2014) (6)
Nonlinear Donati compatibility conditions for the nonlinear Kirchhoff–von Kármán–Love plate theory (2013) (6)
2. Introduction to the Finite Element Method (2002) (6)
Partial Differential Equations: Theory, Control and Approximation (2014) (5)
Numerical analysis of the generalized von Kármán equations (2005) (5)
A new approach to the fundamental theorem of surface theory, by means of the Darboux-Vallée-Fortuné compatibility relation (2009) (5)
Rotation fields and the fundamental theorem of Riemannian geometry in R3 (2006) (5)
Discrete variational Green's function. I (1970) (5)
Two-Dimensional Approximations of Three-Dimensional Models in Nonlinear Plate Theory (1981) (5)
New formulations of linearized elasticity problems, based on extensions of Donati's theorem (2006) (5)
On Questions of Existence in Shell Theory (1976) (5)
A surface in W2, is a locally Lipschitz-continuous function of its fundamental forms in W1, and L, p > 2 (2019) (5)
Nonlinear Donati compatibility conditions and the intrinsic approach for nonlinearly elastic plates (2015) (5)
A generalization of the classical CesroVolterra path integral formula (2009) (5)
New compatibility conditions for the fundamental theorem of surface theory (2007) (4)
3. Conforming Finite Element Methods for Second-Order Problems (2002) (4)
Up to isometries, a deformation is a continuous function of its metric tensor (2002) (4)
A surface is a continuous function of its two fundamental forms (2002) (4)
Asymptotic methods for elastic structures : proceedings of the international conference, Lisbon, Portugal, October 4-8, 1993 (1995) (4)
An intrinsic approach and a notion of polyconvexity for nonlinearly elastic plates (2012) (4)
Donati compatibility conditions on a surface Application to shell theory (2014) (4)
Nonlinear Shell Models of Koiter’s Type (2018) (4)
An intrinsic formulation of the Kirchhoff–Love theory of linearly elastic plates (2017) (4)
The intrinsic theory of linearly elastic plates (2018) (4)
Up to isometries, a deformation is a continuous function of its metric tensor (2002) (4)
New estimates of the distance between two surfaces in terms of the distance between their fundamental forms (2019) (4)
On the recovery of a manifold with boundary in Rn (2004) (3)
Asymptotic justification of the intrinsic equations of Koiter's model of a linearly elastic shell (2019) (3)
Linear and Nonlinear Functional Analysis with Applications - with 401 Problems and 52 Figures (2013) (3)
Chapter 4 - Nonlinearly Elastic Plates (1997) (3)
Solution of equations in R[n] (part 4) ; Techniques of scientific computing (part 4) ; Numerical methods for fluids (part 2) (2002) (3)
Mathematical Shell Theory: Recent Developments and Open Problems (1994) (3)
On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity (2003) (3)
Mathematical elasticity: General preface (2000) (3)
8. Finite Element Methods for Shells (2002) (3)
ASYMPTOTIC ANALYSIS OF ELASTIC SHELLS (1997) (3)
Recovery of immersions from their metric tensors and nonlinear Korn inequalities: A brief survey (2017) (3)
Chapter 5 - The Von Kármán Equations (1997) (3)
Recovery of a displacement field on a surface from its linearized change of metric and change of curvature tensors (2007) (2)
An O(h2) method for a non-smooth boundary value problem (1968) (2)
Preface to volume II (1997) (2)
Operator equations and duality mappings in Sobolev spaces with variable exponents (2013) (2)
Finite-Element Method (1992) (2)
Partial differential equations : theory, control and approximation : in honor of the scientific heritage of Jacques-Louis Lions (2014) (2)
Greenʼs formulas with little regularity on a surface – Application to Donati-like compatibility conditions on a surface (2013) (2)
A brief introduction to mathematical shell theory (2008) (2)
7. A Mixed Finite Element Method (2002) (2)
Extension of a Riemannian metric with vanishing curvature (2004) (2)
Essential numerical methods in electromagnetics : a derivative of handbook of numerical analysis, special volume: numerical methods in electromagnetics, vol XIII (2011) (2)
W2,p-estimates for surfaces in terms of their two fundamental forms (2017) (2)
Nonlinear Donati compatibility conditions on a surface — Application to the intrinsic approach for Koiter’s model of a nonlinearly elastic shallow shell (2017) (2)
Continuity in Fréchet topologies of a surface as a function of its fundamental forms (2020) (2)
Nonlinear Saint-Venant compatibility conditions for nonlinearly elastic plates (2011) (2)
Mathematical Modelling and Numerical Methods in Finance, Volume 15: Special Volume (Handbook of Numerical Analysis) (2009) (2)
Expression of Dirichlet boundary conditions in terms of the strain tensor in linearized elasticity (2013) (2)
1. Elliptic Boundary Value Problems (2002) (2)
Explicit reconstruction of a displacement field on a surface by means of its linearized change of metric and change of curvature tensors (2008) (2)
LINEARIZED ELASTICITY AND KORN'S INEQUALITY REVISITED (2004) (2)
Mathematical Modeling and Numerical Analysis of Linearly Elastic Shells (1995) (2)
The space on a surface – Application to Donati-like compatibility conditions on a surface (2013) (2)
Proceedings of the international conference on Asymptotic methods for elastic structures (1995) (2)
Locally Convex Spaces and Harmonic Analysis: An Introduction (2021) (2)
On rigid displacements and their relation to the infinitesimal rigid displacement lemma in shell theory (2003) (2)
An Introduction to Differential Geometry in ℝ3 (2008) (2)
SHELLS. Mathematical modeling and scientific computing (1997) (1)
Saint Venant compatibility equations on a surface-Application to linear intrinsic shell theory (2019) (1)
Mathematical Problems in Mechanics A generalization of the classical Cesàro-Volterra path integral formula (2009) (1)
Finite element (Part 2); Numerical methods for solids (Part 2) (1996) (1)
Solution of equations in Rn (Part 3); Techniques of scientific computer (Part 3) (2000) (1)
Chapter 1 - Linearly Elastic Plates (1997) (1)
Numerical methods of high-order accuracy for nonlinear boundary value problems (1968) (1)
Continuity in H1-norms of surfaces in terms of the L1-norms of their fundamental forms (2005) (1)
On the convergence of incremental methods in finite elasticity (1982) (1)
5. Application of the Finite Element Method to Some Nonlinear Problems (2002) (1)
Intrinsic formulation of the displacement-traction problem in linear shell theory (2018) (1)
Recovery of a displacement field from its linearized strain tensor field in curvilinear coordinates (2007) (1)
Techniques of scientific computing (Part 1);Numerical methods for solids (Part 1); Solution of equations in Rn (Part 2) (1994) (1)
Expression of Dirichlet boundary conditions in terms of the Cauchy–Green tensor field (2013) (1)
Applications of multiple scaling in mechanics : proceedings, international conference Ecole normale supérieure, Paris November, 24-28, 1986 = Applications des échelles multiples en mécanique (1987) (1)
Which is Implicitly Defined By an Underdetermined System of Equations. (0)
Direct Computation of Stresses in Elasticity (2014) (0)
Intrinsic formulation of the Kirchhoff–Love theory of nonlinearly elastic plates (2022) (0)
Shell models : old and new (2011) (0)
Applications of Mathematics E. G. Ladopoulos; V. A. Zisis Existence and uniqueness for non-linear singular integral equations used in fluid mechanics (2020) (0)
Continuity of a surface in Fréchet spaces (2019) (0)
4. Other Finite Element Methods for Second-Order Problems (2002) (0)
Richard Steven Varga, 1928–2022 (2022) (0)
Author's reply to the review of Introduction to Numerical Linear Algebra and Optimisation (P. G. Ciarlet) (1992) (0)
A finite element method for intrinsic elasticity (2015) (0)
Interpolation Error Estimates for the Reduced (2010) (0)
Shells : mathematical modelling and scientific computing: International Conference of Shells (Santiago de Compostela, 14-18 July 1997) (1997) (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)
AND CRISTINEL MARDARE and the Christoffel symbols of the second kind Γ ταβ associated with the matrix field (0)
Chapter 3 - Linearly Elastic Shallow Shells in Cartesian Coordinates (1997) (0)
Finite-Difference Method (1992) (0)
Chapter 2 - Junctions in Linearly Elastic Multi-Structures (1997) (0)
On a vector version of a fundamental Lemma of J. L. Lions (2018) (0)
Mathematical justification of linear shallow shell models by an asymptotic analysis (1991) (0)
Mathematical Problems in Mechanics Legendre-Fenchel duality in elasticity (2017) (0)
Mathematical Problems in Mechanics/Differential Geometry Continuity in H 1 -norms of surfaces in terms of the L 1 -norms of their fundamental forms (2005) (0)
Existence theory for linearly elastic shells (1994) (0)
Numerical methods for solids (part 3) . Numerical methods for fluids (part 1) (1998) (0)
New identity and Korn's inequalities on a surface (2015) (0)
Foundations of computational mathematics: special volume (2003) (0)
Operator equations and duality mappings in Sobolev spaces with variable exponents (2013) (0)
AN OBSTACLE PROBLEM FOR FLEXURAL SHELLS (2021) (0)
Intrinsic Formulation of the Kirchhoff-Love Theory of Nonlinearly Elastic Shallow Shells (2022) (0)
Mathematical Problems in Mechanics A Lagrangian approach to intrinsic linearized elasticity (2010) (0)
Preface to Volume I11This “Preface to Volume I” is an updated excerpt from the “Preface” to the first edition (1988) of Volume I. (1997) (0)
Recovery of immersions from their metric tensors and nonlinear Korn inequalities: A brief survey (2017) (0)
Jacques-Louis Lions. 2 May 1928 – 17 May 2001 (2002) (0)
Preface to volume I (1997) (0)
Special topics of applied mathematics. Edited by J. Frehse, D. Pallaschke, U. Trottenberg, North-Holland, Amsterdam, 1980 (1981) (0)
Intrinsic finite element methods for the computation of fluxes for Poisson’s equation (2015) (0)
Preface to Volume III1 (2000) (0)
Review: T. Valent, Boundary value problems of finite elasticity (1990) (0)
Some Mathematical Aspects of Three-Dimensional Elasticity (1983) (0)
Classical vs. intrinsic shell theory (2011) (0)
On the Brachistochrone Problem (2022) (0)
Description of Three-Dimensional Elasticity (1983) (0)

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