Bernardo J. Cockburn

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Mathematics

Bernardo J. Cockburn's Degrees

PhD Mathematics University of Texas at Austin
Masters Mathematics University of Texas at Austin
Bachelors Mathematics University of Texas at Austin

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Bernardo J. Cockburn's Published Works

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Published Works

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems (2001) (3263)
TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework (1989) (2255)
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems (1998) (2185)
The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multi-D systems (1998) (1842)
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems (2001) (1755)
The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case (1990) (1614)
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems (1989) (1487)
Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems (2009) (1086)
The Development of Discontinuous Galerkin Methods (2000) (926)
Discontinuous Galerkin methods (2003) (787)
Discontinuous Galerkin Methods: Theory, Computation and Applications (2011) (593)
The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws (1991) (530)
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems (2000) (528)
The Runge-Kutta local projection discontinous Galerkin finite element method for conservation laws (1990) (408)
Discontinuous Galerkin Methods for Convection-Dominated Problems (1999) (382)
Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids (2001) (334)
A locally conservative LDG method for the incompressible Navier-Stokes equations (2004) (305)
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations (2004) (303)
Discontinuous Galerkin Methods for Elliptic Problems (2000) (281)
An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations (2009) (281)
The Runge-Kutta local projection P1-discontinuous-Galerkin finite element method for scalar conservation laws (1988) (280)
An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations (2009) (280)
Advanced Numerical Approximation of Nonlinear Hyperbolic Equations (1998) (275)
Local Discontinuous Galerkin Methods for the Stokes System (2002) (269)
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems (2008) (268)
A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier–Stokes Equations (2007) (252)
A projection-based error analysis of HDG methods for Timoshenko beams (2010) (251)
An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations (2011) (251)
Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems (2002) (238)
An introduction to the Discontinuous Galerkin method for convection-dominated problems (1998) (223)
A hybridizable discontinuous Galerkin method for Stokes flow (2010) (223)
Analysis of HDG methods for Stokes flow (2010) (186)
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations (2003) (178)
A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems (2009) (177)
To CG or to HDG: A Comparative Study (2012) (177)
Superconvergent discontinuous Galerkin methods for second-order elliptic problems (2009) (173)
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods (2016) (166)
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics (2011) (158)
Stabilization mechanisms in discontinuous Galerkin finite element methods (2006) (158)
A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems (2004) (151)
A Hybridizable Discontinuous Galerkin Method for the Compressible Euler and Navier-Stokes Equations (2010) (131)
A new elasticity element made for enforcing weak stress symmetry (2010) (131)
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations (2011) (130)
The Derivation of Hybridizable Discontinuous Galerkin Methods for Stokes Flow (2009) (124)
Nonlinearly stable compact schemes for shock calculations (1994) (123)
Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension (2007) (120)
A hybridizable discontinuous Galerkin method for linear elasticity (2009) (118)
Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems (1997) (114)
An error estimate for finite volume methods for multidimensional conservation laws (1994) (114)
The local discontinuous Galerkin method for the Oseen equations (2003) (111)
An Analysis of the Minimal Dissipation Local Discontinuous Galerkin Method for Convection–Diffusion Problems (2007) (110)
Some Extensions Of The Local Discontinuous Galerkin Method For Convection-Diffusion Equations In Mul (1999) (110)
A Mixed Finite Element Method for Elasticity in Three Dimensions (2005) (109)
Hybridized globally divergence-free LDG methods. Part I: The Stokes problem (2005) (105)
The local projection $P^0-P^1$ -discontinuous-Galerkin finite element method for scalar conservation laws (1989) (101)
The local discontinuous Galerkin method for contaminant transport (2000) (100)
Conditions for superconvergence of HDG methods for second-order elliptic problems (2012) (99)
Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations (1999) (96)
High-order RKDG Methods for Computational Electromagnetics (2005) (95)
Static Condensation, Hybridization, and the Devising of the HDG Methods (2016) (94)
Convergence of the finite volume method for multidimensional conservation laws (1995) (92)
Devising discontinuous Galerkin methods for non-linear hyperbolic conversation laws (2001) (92)
Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes (2008) (91)
Divergence-conforming HDG methods for Stokes flows (2014) (91)
Error estimates for finite element methods for scalar conservation laws (1996) (88)
A Comparison of HDG Methods for Stokes Flow (2010) (86)
Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations (2016) (85)
A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains (2012) (85)
A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations (2013) (83)
Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode at 300 K (1995) (80)
Hybridizable Discontinuous Galerkin Methods (2011) (79)
Multigrid for an HDG method (2013) (78)
An A Posteriori Error Estimate for the Local Discontinuous Galerkin Method Applied to Linear and Nonlinear Diffusion Problems (2005) (76)
Discontinuous Galerkin Methods for Computational Fluid Dynamics (2004) (74)
Incompressible Finite Elements via Hybridization. Part I: The Stokes System in Two Space Dimensions (2005) (73)
The embedded discontinuous Galerkin method: application to linear shell problems (2007) (72)
An Analysis of the Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems (2009) (71)
Locally Conservative Fluxes for the Continuous Galerkin Method (2007) (70)
Discontinuous Galerkin methods for incompressible elastic materials (2006) (69)
The local discontinuous Galerkin method for linearized incompressible fluid flow: a review (2005) (69)
Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation (1995) (66)
An Equal-Order DG Method for the Incompressible Navier-Stokes Equations (2009) (66)
A hybridizable discontinuous Galerkin formulation for non-linear elasticity (2015) (65)
Analysis of variable-degree HDG methods for convection–diffusion equations. Part I: general nonconforming meshes (2012) (64)
Superconvergence by M-decompositions. Part I: General theory for HDG methods for diffusion (2016) (62)
A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems (2009) (62)
Error analysis of variable degree mixed methods for elliptic problems via hybridization (2005) (61)
Superconvergent HDG methods for linear elasticity with weakly symmetric stresses (2013) (60)
A hybridizable discontinuous Galerkin method for fractional diffusion problems (2014) (58)
An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation (2016) (58)
A Model Numerical Scheme for the Propagation of phase Transitions in Solids (1996) (53)
Devising HDG methods for Stokes flow: An overview (2014) (53)
An Embedded Discontinuous Galerkin Method for the Compressible Euler and Navier-Stokes Equations (2011) (52)
A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach (1996) (52)
Approximation of the Velocity by Coupling Discontinuous Galerkin and Mixed Finite Element Methods for Flow Problems (2002) (51)
Analysis of variable-degree HDG methods for Convection-Diffusion equations. Part II: Semimatching nonconforming meshes (2013) (51)
Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains (2012) (51)
Analysis of HDG Methods for Oseen Equations (2013) (50)
A hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations (2010) (49)
Uniform-in-time superconvergence of HDG methods for the heat equation (2012) (48)
A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity (2013) (46)
A class of embedded discontinuous Galerkin methods for computational fluid dynamics (2015) (46)
Analysis of an HDG method for linear elasticity (2015) (45)
Incompressible Finite Elements via Hybridization. Part II: The Stokes System in Three Space Dimensions (2005) (45)
A Simple Introduction to Error Estimation for Nonlinear Hyperbolic Conservation Laws (1999) (43)
The Staggered DG Method is the Limit of a Hybridizable DG Method. Part II: The Stokes Flow (2014) (42)
Local derivative post-processing for the discontinuous Galerkin method (2009) (42)
The local projection P0-P1-discontinuous-Galerkin finite element method for scalar conservation laws (1989) (42)
A Posteriori Error Estimates for HDG Methods (2012) (41)
Superconvergence by M-decompositions. Part III: Construction of three-dimensional finite elements∗ (2017) (41)
A Hybridizable Discontinuous Galerkin Method for the p-Laplacian (2016) (38)
Superconvergence by M-decompositions. Part II: Construction of two-dimensional finite elements (2017) (38)
Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation (2013) (38)
Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems (2014) (37)
Stormer-Numerov HDG Methods for Acoustic Waves (2018) (37)
A Posteriori Error Analysis for Hybridizable Discontinuous Galerkin Methods for Second Order Elliptic Problems (2013) (37)
Error Estimates for the Runge-Kutta Discontinuous Galerkin Method for the Transport Equation with Discontinuous Initial Data (2008) (37)
A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation (2015) (36)
An accurate spectral/discontinuous finite-element formulation of a phase-space-based level set approach to geometrical optics (2005) (36)
Conditions for superconvergence of HDG methods for Stokes flow (2012) (35)
Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by $M$-decompositions (2017) (34)
Post-Processing of Galerkin Methods for Hyperbolic Problems (2000) (33)
Determining degrees of freedom for nonlinear dissipative equations (1995) (33)
Hybridizable Discontinuous Galerkin Methods for Timoshenko Beams (2010) (33)
Locking-Free Optimal Discontinuous Galerkin Methods for Timoshenko Beams (2006) (32)
A Priori Error Estimates for Numerical Methods for Scalar Conservation Laws Part III: Multidimensional Flux-Splitting Monotone Schemes on Non-Cartesian Grids (1998) (32)
A posteriori error estimates for general numerical methods for scalar conservation laws (1994) (32)
Solving Convection-Diffusion Problems on Curved Domains by Extensions from Subdomains (2013) (31)
New hybridization techniques (2005) (31)
An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions (2012) (30)
A priori error estimates for numerical methods for scalar conservation laws. Part II : flux-splitting monotone schemes on irregular Cartesian grids (1997) (29)
The P(1-) RKDG Method for Two-Dimensional Euler Equations of Gas Dynamics (1991) (29)
On Convergence to Entropy Solutions of A Single Conservation Law (1996) (29)
Symplectic Hamiltonian HDG methods for wave propagation phenomena (2017) (28)
Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains (2010) (28)
Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity (2010) (28)
Design and development of a discontinuous Galerkin method for shells (2006) (28)
The Local Projection P0P1-Discontinuous-Galerkin-Finite Element Method for Scalar Conservation Laws (1987) (27)
Continuous dependence and error estimation for viscosity methods (2003) (27)
Analysis of a finite element method for the drift-diffusion semiconductor device equations: the multidimensional case (1995) (27)
The Staggered DG Method is the Limit of a Hybridizable DG Method. Part II: The Stokes Flow (2016) (27)
Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension (2016) (26)
Advanced numerical approximation of nonlinear hyperbolic equations : lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 23-28, 1997 (1998) (26)
Superconvergent HDG Methods on Isoparametric Elements for Second-Order Elliptic Problems (2012) (26)
A note on the devising of superconvergent HDG methods for Stokes flow by M-decompositions (2016) (25)
A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. Part I: The steady state case (2002) (24)
Interpolatory HDG Method for Parabolic Semilinear PDEs (2018) (22)
Local discontinuous Galerkin methods for elliptic problems (2001) (21)
A Systematic Construction of Finite Element Commuting Exact Sequences (2016) (20)
Coupling at a Distance HDG and BEM (2012) (20)
Hybridization and Postprocessing Techniques for Mixed Eigenfunctions (2010) (19)
Quasimonotone Schemes for Scalar Conservation Laws. Part II (1990) (18)
Convergence of finite volume methods (1991) (18)
The devising of symmetric couplings of boundary element and discontinuous Galerkin methods (2012) (17)
Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Timoshenko Beams (2006) (16)
An a posteriori error estimate for the variable-degree Raviart-Thomas method (2013) (15)
Space-Time Hybridizable Discontinuous Galerkin Method for the Advection–Diffusion Equation on Moving and Deforming Meshes (2013) (15)
An adaptive method with rigorous error control for the Hamilton--Jacobi equations. Part I: The one-dimensional steady state case (2005) (14)
Divergence-Free HDG Methods for the Vorticity-Velocity Formulation of the Stokes Problem (2012) (13)
Commuting diagrams for the TNT elements on cubes (2013) (13)
Convergence of a finite element method for the drift-diffusion semiconductor device equations (1992) (13)
Coupling of Raviart-Thomas and Hybridizable Discontinuous Galerkin Methods with BEM (2012) (13)
Superconvergent Interpolatory HDG Methods for Reaction Diffusion Equations I: An HDGk Method (2019) (13)
Error estimates for a finite element method for the drift-diffusion semiconductor device equations (1994) (12)
Contraction property of adaptive hybridizable discontinuous Galerkin methods (2015) (12)
The Quasi-Monotone Schemes for Scalar Conservation Laws, Part III (1986) (11)
A new discontinuous Galerkin method, conserving the discrete H2-norm, for third-order linear equations in one space dimension (2016) (11)
HDG Methods for Hyperbolic Problems (2016) (11)
Discontinuous Galerkin Methods for Timoshenko Beams (2004) (11)
An algorithm for stabilizing hybridizable discontinuous Galerkin methods for nonlinear elasticity (2019) (11)
The hybridizable discontinuous Galerkin methods (2011) (11)
Continuous Dependence on the Nonlinearity of Viscosity Solutions of Parabolic Equations (2001) (11)
Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces (2016) (11)
Adjoint-Based, Superconvergent Galerkin Approximations of Linear Functionals (2017) (10)
On the Continuity in BV (Ω) of the L 2 -Projection into Finite Element Spaces (1991) (10)
Error estimates for a finite element method for the drift-diffusion semiconductor device equations: the zero diffusion case (1994) (8)
Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws III : One-Dimensional Systems (2003) (8)
The Local Discontinuous Galerkin Method for Contaminant Transport Problems (2000) (8)
Symplectic Hamiltonian finite element methods for linear elastodynamics (2021) (7)
Finite Element Computation of the Hydrodynamic Model of Semiconductor Devices (1993) (7)
An adaptive high-order discontinuous Galerkin method with error control for the Hamilton-Jacobi equations. Part I: The one-dimensional steady state case (2007) (7)
An adaptive method with rigorous error control for the Hamilton-Jacobi equations. Part II: The two-dimensional steady-state case (2005) (7)
Maxwell equations on polarizable media (1988) (6)
Numerical solution of Maxwell's equations in a conductive and polarizable medium (1989) (6)
Numerical Resolution of Maxwell's Equations in Polarisable Media at Radio and Lower Frequencies (1985) (6)
Two new techniques for generating exactly incompressible approximate velocities (2009) (5)
Adjoint Recovery of Superconvergent Linear Functionals from Galerkin Approximations. The One-dimensional Case (2007) (4)
Discontinuous Galerkin methods through the lens of variational multiscale analysis (2022) (4)
LDG methods for Stokes flow problems (2003) (4)
Foreword (2009) (4)
Solving Convection-Diffusion Problems on Curved Domains by Extensions from Subdomains (2013) (3)
Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations (2012) (3)
The TVD-Projection Method for Solving Implicit Numeric Schemes for Scalar Conservation Laws: A Numerical Study of a Simple Case (1987) (3)
The pursuit of a dream, Francisco Javier Sayas and the HDG methods (2021) (3)
Supercloseness of Primal-Dual Galerkin Approximations for Second Order Elliptic Problems (2018) (3)
Supplement to Convergence of a Finite Element Method for the Drift- Diffusion Semiconductor Device Equations: The Zero Diffusion Case (1992) (3)
The local discontinuous Galerkin methods for linear incompressible flow: A review (2003) (3)
Discrete H1-Inequalities for Spaces Admitting M-Decompositions (2018) (3)
Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems (2015) (2)
The Weak Galerkin methods are rewritings of the Hybridizable Discontinuous Galerkin methods (2018) (2)
Justification théorique d'une méthode de résolution des équations de Maxwell en milieu polarisable (1984) (2)
A total variation diminishing-projection method for solving implicit numerical schemes for scalar conservation laws: a numerical study of a simple case (1989) (2)
Le schema G-k/2 pour les lois de conservation scalaires (1985) (2)
An a priori error analysis of adjoint-based super-convergent Galerkin approximations of linear functionals (2021) (2)
Influence of tissue viscoelasticity on the optic nerve head perfusion: a mathematical model (2016) (2)
The Local Discontinuous Galerkin Method in Incompressible Fluid Flow (2)
The local discontinuous Galerkin method and component design integration for 3D elasticity (2005) (2)
Discontinuous Galerkin Methods with Time-Operators in Their Numerical Traces for Time-Dependent Electromagnetics (2022) (2)
An adjoint-based adaptive error approximation of functionals by the hybridizable discontinuous Galerkin method for second-order elliptic equations (2022) (1)
An a priori-a posteriori approach to numerical conservation laws (1996) (1)
Interpolatory HDG Method for Parabolic Semilinear PDEs (2019) (1)
A Priori Error Estimates for Nonlinear Scalar Conservation Laws (1999) (1)
The Utility of Modeling and Simulation in Determining Transport Performance Properties of Semiconductors (2000) (1)
Discontinuous Galerkin methods Plenary lecture presented at the 80 th Annual GAMM Conference , Augsburg , 25 – 28 March 2002 (2003) (1)
ON THE CONTINUITY IN BV(ß) OF THE L -PROJECTION INTO FINITE ELEMENT SPACES (2010) (1)
The Computation of a Locally Conservative Stress for the Continuous Galerkin Method for Compressible Linearly Elastic Materials (2008) (1)
An Introduction to the Theory of M -Decompositions (2018) (1)
Symplectic Hamiltonian finite element methods for electromagnetics (2022) (1)
Superconvergent Interpolatory HDG Methods for Reaction Diffusion Equations II: HHO-Inspired Methods (2020) (0)
Post-processing for spatial accuracy-enhancement of pure Lagrange–Galerkin schemes applied to convection-diffusion equations (2020) (0)
ICASE NONLINEARLY STABLE COMPACT SCHEMES FOR SHOCK CALCULATIONS DTIC _ ELECTE (0)
Mesoscale ocean dynamics modeling (1996) (0)
Aeroheating Predictions of Hypersonic Flight Geometries with High-Order Discontinuous Galerkin Methods (2023) (0)
Analysis of HDG Methods for Oseen Equations (2012) (0)
To CG or to HDG: A Comparative Study (2011) (0)
r ICASE Report No . 91-32 ADA 236 842 ICASE THE P L-RKDG METHOD FOR TWO-DIMENSIONAL EULER EQUATIONS OF GAS DYNAMICS (0)
A Posteriori Error Estimates for HDG Methods (2011) (0)
An adjoint-based super-convergent Galerkin approximation of eigenvalues (2021) (0)
Divergence-Free HDG Methods for the Vorticity-Velocity Formulation of the Stokes Problem (2011) (0)
Superconvergence of hp-discontinuous Galerkin methods for convection-diffusion problems (2005) (0)
Discontinuous Galerkin Methods for Partial Differential Equations (2008) (0)
THE STAGGERED DG METHOD FOR THE STOKES FLOW IS THE LIMIT OF A HYBRIDIZABLE DG METHOD (2014) (0)
Supercloseness of Primal-Dual Galerkin Approximations for Second Order Elliptic Problems (2017) (0)
HYBRIDIZABLE DISCONTINUOUS GALERKIN METHODS FOR CONTINUUM MECHANICS (2013) (0)
A Priori Estimates of Solution of a Homogeneous Boundary Value Problem for Parabolic Type Equations by the Discontinuous Galerkin Method on Staggered Grids (2017) (0)
An adaptive spectral/DG method for a reduced phase-space based level set approach to geometrical optics on curved elements (2014) (0)
Stormer-Numerov HDG Methods for Acoustic Waves (2017) (0)
Applications of the integral averaging bifurcation method to retarded functional differential equations (1980) (0)
New Results in Numerical Conservation Laws (2019) (0)
Adjoint-Based, Superconvergent Galerkin Approximations of Linear Functionals (2017) (0)
A hybridizable discontinuous Galerkin method for fractional diffusion problems (2014) (0)
1. g From finite differences to finite elements: A short history of numerical analysis of partial differential (2003) (0)
Locking-free hp-discontinuous Galerkin methods for Timoshenko beams (2005) (0)
Acta Numerica 2003: Continuous dependence and error estimation for viscosity methods (2003) (0)
Hybridization and Postprocessing Techniques for (2010) (0)
A new approach to numerical conservation laws (1995) (0)
Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems (2023) (0)
- Discontinuous Galerkin methods for equations with divergence-free solutions: preliminary results (2003) (0)

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Published Works

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Bernardo J. Cockburn's AcademicInfluence.com Rankings