Bernardo Cockburn

ORCID

Publication Activity (10 Years)

Years Active: 1993-2023
Publications (10 Years): 22

Top Venues

Publications

Bernardo Cockburn, Shukai Du, Manuel A. Sánchez
Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems. Frontiers Appl. Math. Stat. 9 (2023)
Sreevatsa Anantharamu, Bernardo Cockburn
Efficient implementation of the hybridized Raviart-Thomas mixed method by converting flux subspaces into stabilizations. CoRR (2023)
Bernardo Cockburn, Shiqiang Xia
An adjoint-based super-convergent Galerkin approximation of eigenvalues. J. Comput. Phys. 449 (2022)
Bernardo Cockburn, Shukai Du, Manuel A. Sánchez
Discontinuous Galerkin Methods with Time-Operators in Their Numerical Traces for Time-Dependent Electromagnetics. Comput. Methods Appl. Math. 22 (4) (2022)
Bernardo Cockburn, Shiqiang Xia
An adjoint-based adaptive error approximation of functionals by the hybridizable discontinuous Galerkin method for second-order elliptic equations. J. Comput. Phys. 457 (2022)
Gang Chen, Bernardo Cockburn, John R. Singler, Yangwen Zhang
Superconvergent Interpolatory HDG methods for reaction diffusion equations II: HHO-inspired methods. CoRR (2020)
Bernardo Cockburn, John R. Singler, Yangwen Zhang
Interpolatory HDG Method for Parabolic Semilinear PDEs. J. Sci. Comput. 79 (3) (2019)
Gang Chen, Bernardo Cockburn, John R. Singler, Yangwen Zhang
Method. J. Sci. Comput. 81 (3) (2019)
Bernardo Cockburn, Zhixing Fu, Allan Hungria, Liangyue Ji, Manuel A. Sánchez, Francisco-Javier Sayas
Stormer-Numerov HDG Methods for Acoustic Waves. J. Sci. Comput. 75 (2) (2018)
Bernardo Cockburn, Guosheng Fu, Weifeng Qiu
-Inequalities for Spaces Admitting M-Decompositions. SIAM J. Numer. Anal. 56 (6) (2018)
Bernardo Cockburn, Manuel A. Sánchez, Chunguang Xiong
Supercloseness of Primal-Dual Galerkin Approximations for Second Order Elliptic Problems. J. Sci. Comput. 75 (1) (2018)
Manuel A. Sánchez, C. Ciuca, Ngoc Cuong Nguyen, Jaime Peraire, Bernardo Cockburn
Symplectic Hamiltonian HDG methods for wave propagation phenomena. J. Comput. Phys. 350 (2017)
Ayçil Çesmelioglu, Bernardo Cockburn, Weifeng Qiu
Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations. Math. Comput. 86 (306) (2017)
Bernardo Cockburn, Guosheng Fu, Francisco-Javier Sayas
Superconvergence by M-decompositions. Part I: General theory for HDG methods for diffusion. Math. Comput. 86 (306) (2017)
Bernardo Cockburn, Guosheng Fu
A Systematic Construction of Finite Element Commuting Exact Sequences. SIAM J. Numer. Anal. 55 (4) (2017)
Bernardo Cockburn, Zhu Wang
Adjoint-Based, Superconvergent Galerkin Approximations of Linear Functionals. J. Sci. Comput. 73 (2-3) (2017)
Bernardo Cockburn, Jiguang Shen
A Hybridizable Discontinuous Galerkin Method for the p-Laplacian. SIAM J. Sci. Comput. 38 (1) (2016)
Bernardo Cockburn, Ricardo H. Nochetto, Wujun Zhang
Contraction property of adaptive hybridizable discontinuous Galerkin methods. Math. Comput. 85 (299) (2016)
Kassem Mustapha, Maher Nour, Bernardo Cockburn
Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems. Adv. Comput. Math. 42 (2) (2016)
Bernardo Cockburn, Alan Demlow
Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces. Math. Comput. 85 (302) (2016)
Eric T. Chung, Bernardo Cockburn, Guosheng Fu
The Staggered DG Method is the Limit of a Hybridizable DG Method. Part II: The Stokes Flow. J. Sci. Comput. 66 (2) (2016)
Yanlai Chen, Bernardo Cockburn, Bo Dong
Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension. Math. Comput. 85 (302) (2016)
Ngoc Cuong Nguyen, Jaime Peraire, Bernardo Cockburn
A class of embedded discontinuous Galerkin methods for computational fluid dynamics. J. Comput. Phys. 302 (2015)
Bernardo Cockburn, Kassem Mustapha
A hybridizable discontinuous Galerkin method for fractional diffusion problems. Numerische Mathematik 130 (2) (2015)
Ngoc Cuong Nguyen, Jaime Peraire, Fernando Reitich, Bernardo Cockburn
A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation. J. Comput. Phys. 290 (2015)
Bernardo Cockburn, Weifeng Qiu, Manuel Solano
A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity. Math. Comput. 83 (286) (2014)
Bernardo Cockburn, Chiu-Yen Kao, Fernando Reitich
An adaptive spectral/DG method for a reduced phase-space based level set approach to geometrical optics on curved elements. J. Comput. Phys. 259 (2014)
Yanlai Chen, Bernardo Cockburn
Analysis of variable-degree HDG methods for Convection-Diffusion equations. Part II: Semimatching nonconforming meshes. Math. Comput. 83 (285) (2014)
Bernardo Cockburn, Weifeng Qiu
Commuting diagrams for the TNT elements on cubes. Math. Comput. 83 (286) (2014)
Bernardo Cockburn, Manuel Solano
Solving Convection-Diffusion Problems on Curved Domains by Extensions from Subdomains. J. Sci. Comput. 59 (2) (2014)
Bernardo Cockburn, Wujun Zhang
An a posteriori error estimate for the variable-degree Raviart-Thomas method. Math. Comput. 83 (287) (2014)
Eric T. Chung, Bernardo Cockburn, Guosheng Fu
The Staggered DG Method is the Limit of a Hybridizable DG Method. SIAM J. Numer. Anal. 52 (2) (2014)
Bernardo Cockburn, Vincent Quenneville-Bélair
Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. Math. Comput. 83 (285) (2014)
Bernardo Cockburn, Francisco-Javier Sayas
Divergence-conforming HDG methods for Stokes flows. Math. Comput. 83 (288) (2014)
Sander Rhebergen, Bernardo Cockburn, Jaap J. W. van der Vegt
A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations. J. Comput. Phys. 233 (2013)
Ayçil Çesmelioglu, Bernardo Cockburn, Ngoc Cuong Nguyen, Jaume Peraire
Analysis of HDG Methods for Oseen Equations. J. Sci. Comput. 55 (2) (2013)
Bernardo Cockburn, Wujun Zhang
A Posteriori Error Analysis for Hybridizable Discontinuous Galerkin Methods for Second Order Elliptic Problems. SIAM J. Numer. Anal. 51 (1) (2013)
Bernardo Cockburn, Ke Shi
Conditions for superconvergence of HDG methods for Stokes flow. Math. Comput. 82 (282) (2013)
Bernardo Cockburn, Ivan Merev, Jianliang Qian
Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations. Math. Comput. 82 (281) (2013)
Bernardo Cockburn, Weifeng Qiu, Ke Shi
Conditions for superconvergence of HDG methods for second-order elliptic problems. Math. Comput. 81 (279) (2012)
Bernardo Cockburn, Jintao Cui
Divergence-Free HDG Methods for the Vorticity-Velocity Formulation of the Stokes Problem. J. Sci. Comput. 52 (1) (2012)
Sander Rhebergen, Bernardo Cockburn
A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. J. Comput. Phys. 231 (11) (2012)
Bernardo Cockburn, Wujun Zhang
A Posteriori Error Estimates for HDG Methods. J. Sci. Comput. 51 (3) (2012)
Fatih Celiker, Bernardo Cockburn, Ke Shi
A projection-based error analysis of HDG methods for Timoshenko beams. Math. Comput. 81 (277) (2012)
Bernardo Cockburn, Jintao Cui
An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions. Math. Comput. 81 (279) (2012)
Bernardo Cockburn, Francisco-Javier Sayas, Manuel Solano
Coupling at a Distance HDG and BEM. SIAM J. Sci. Comput. 34 (1) (2012)
Brandon Chabaud, Bernardo Cockburn
Uniform-in-time superconvergence of HDG methods for the heat equation. Math. Comput. 81 (277) (2012)
Robert M. Kirby, Spencer J. Sherwin, Bernardo Cockburn
To CG or to HDG: A Comparative Study. J. Sci. Comput. 51 (1) (2012)
Bernardo Cockburn, Manuel Solano
Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains. SIAM J. Sci. Comput. 34 (1) (2012)
Bernardo Cockburn, Johnny Guzmán, Francisco-Javier Sayas
Coupling of Raviart-Thomas and Hybridizable Discontinuous Galerkin Methods with BEM. SIAM J. Numer. Anal. 50 (5) (2012)
Bernardo Cockburn, Weifeng Qiu, Ke Shi
Superconvergent HDG Methods on Isoparametric Elements for Second-Order Elliptic Problems. SIAM J. Numer. Anal. 50 (3) (2012)
Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations. J. Comput. Phys. 230 (19) (2011)
Bernardo Cockburn, Jayadeep Gopalakrishnan, Ngoc Cuong Nguyen, Jaume Peraire, Francisco-Javier Sayas
Analysis of HDG methods for Stokes flow. Math. Comput. 80 (274) (2011)
Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. J. Comput. Phys. 230 (10) (2011)
Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn
An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. J. Comput. Phys. 230 (4) (2011)
Bernardo Cockburn, Deepa Gupta, Fernando Reitich
Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains. J. Sci. Comput. 42 (1) (2010)
Bernardo Cockburn, Jayadeep Gopalakrishnan, F. Li, Ngoc Cuong Nguyen, Jaume Peraire
Hybridization and Postprocessing Techniques for Mixed Eigenfunctions. SIAM J. Numer. Anal. 48 (3) (2010)
Bernardo Cockburn, Jayadeep Gopalakrishnan, Johnny Guzmán
A new elasticity element made for enforcing weak stress symmetry. Math. Comput. 79 (271) (2010)
Bernardo Cockburn, Ngoc Cuong Nguyen, Jaume Peraire
A Comparison of HDG Methods for Stokes Flow. J. Sci. Comput. 45 (1-3) (2010)
Bernardo Cockburn, Bo Dong, Johnny Guzmán, Jianliang Qian
Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity. SIAM J. Numer. Anal. 48 (1) (2010)
Bernardo Cockburn, Jayadeep Gopalakrishnan, Francisco-Javier Sayas
A projection-based error analysis of HDG methods. Math. Comput. 79 (271) (2010)
Fatih Celiker, Bernardo Cockburn, Ke Shi
Hybridizable Discontinuous Galerkin Methods for Timoshenko Beams. J. Sci. Comput. 44 (1) (2010)
Bernardo Cockburn, Chi-Wang Shu
Foreword. J. Sci. Comput. 40 (1-3) (2009)
Bernardo Cockburn, Bo Dong, Johnny Guzmán, Marco Restelli, Riccardo Sacco
A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems. SIAM J. Sci. Comput. 31 (5) (2009)
Bernardo Cockburn, Johnny Guzmán, Haiying Wang
Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Math. Comput. 78 (265) (2009)
Bernardo Cockburn, Jayadeep Gopalakrishnan
The Derivation of Hybridizable Discontinuous Galerkin Methods for Stokes Flow. SIAM J. Numer. Anal. 47 (2) (2009)
Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn
An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. J. Comput. Phys. 228 (9) (2009)
Bernardo Cockburn, Guido Kanschat, Dominik Schötzau
An Equal-Order DG Method for the Incompressible Navier-Stokes Equations. J. Sci. Comput. 40 (1-3) (2009)
Jennifer K. Ryan, Bernardo Cockburn
Local derivative post-processing for the discontinuous Galerkin method. J. Comput. Phys. 228 (23) (2009)
Bernardo Cockburn, Johnny Guzmán, See-Chew Soon, Henry K. Stolarski
An Analysis of the Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems. SIAM J. Numer. Anal. 47 (4) (2009)
Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn
An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. J. Comput. Phys. 228 (23) (2009)
Bernardo Cockburn, Bo Dong, Johnny Guzmán
A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems. J. Sci. Comput. 40 (1-3) (2009)
Bernardo Cockburn, Jayadeep Gopalakrishnan, Raytcho D. Lazarov
Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems. SIAM J. Numer. Anal. 47 (2) (2009)
Bernardo Cockburn, Bo Dong, Johnny Guzmán
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Math. Comput. 77 (264) (2008)
Bernardo Cockburn, Johnny Guzmán
Error Estimates for the Runge-Kutta Discontinuous Galerkin Method for the Transport Equation with Discontinuous Initial Data. SIAM J. Numer. Anal. 46 (3) (2008)
Bernardo Cockburn, Bo Dong, Johnny Guzmán
Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes. SIAM J. Numer. Anal. 46 (3) (2008)
Bernardo Cockburn, Haiying Wang
The Computation of a Locally Conservative Stress for the Continuous Galerkin Method for Compressible Linearly Elastic Materials. J. Sci. Comput. 36 (2) (2008)
Bernardo Cockburn, Bo Dong
An Analysis of the Minimal Dissipation Local Discontinuous Galerkin Method for Convection-Diffusion Problems. J. Sci. Comput. 32 (2) (2007)
Bernardo Cockburn, Guido Kanschat, Dominik Schötzau
A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier-Stokes Equations. J. Sci. Comput. 31 (1-2) (2007)
Bernardo Cockburn, Jayadeep Gopalakrishnan, Haiying Wang
Locally Conservative Fluxes for the Continuous Galerkin Method. SIAM J. Numer. Anal. 45 (4) (2007)
Bernardo Cockburn, Ryuhei Ichikawa
Adjoint Recovery of Superconvergent Linear Functionals from Galerkin Approximations. The One-dimensional Case. J. Sci. Comput. 32 (2) (2007)
Fatih Celiker, Bernardo Cockburn
Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension. Math. Comput. 76 (257) (2007)
Yanlai Chen, Bernardo Cockburn
An adaptive high-order discontinuous Galerkin method with error control for the Hamilton-Jacobi equations. Part I: The one-dimensional steady state case. J. Comput. Phys. 226 (1) (2007)
Fatih Celiker, Bernardo Cockburn, Henry K. Stolarski
Locking-Free Optimal Discontinuous Galerkin Methods for Timoshenko Beams. SIAM J. Numer. Anal. 44 (6) (2006)
Jesús Carrero, Bernardo Cockburn, Dominik Schötzau
Hybridized globally divergence-free LDG methods. Part I: The Stokes problem. Math. Comput. 75 (254) (2006)
Fatih Celiker, Bernardo Cockburn
Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Timoshenko Beams. J. Sci. Comput. 27 (1-3) (2006)
Scot Adams, Bernardo Cockburn
A Mixed Finite Element Method for Elasticity in Three Dimensions. J. Sci. Comput. 25 (3) (2005)
Bernardo Cockburn, Jayadeep Gopalakrishnan
Incompressible Finite Elements via Hybridization. Part II: The Stokes System in Three Space Dimensions. SIAM J. Numer. Anal. 43 (4) (2005)
Bernardo Cockburn, Jayadeep Gopalakrishnan
Error analysis of variable degree mixed methods for elliptic problems via hybridization. Math. Comput. 74 (252) (2005)
Min-Hung Chen, Bernardo Cockburn, Fernando Reitich
High-order RKDG Methods for Computational Electromagnetics. J. Sci. Comput. 22 (1) (2005)
Bernardo Cockburn, Guido Kanschat, Dominik Schötzau
A locally conservative LDG method for the incompressible Navier-Stokes equations. Math. Comput. 74 (251) (2005)
Rommel Bustinza, Gabriel N. Gatica, Bernardo Cockburn
Error Estimate for the Local Discontinuous Galerkin Method Applied to Linear and Nonlinear Diffusion Problems. J. Sci. Comput. 22 (1) (2005)
Bernardo Cockburn, Jayadeep Gopalakrishnan
Incompressible Finite Elements via Hybridization. Part I: The Stokes System in Two Space Dimensions. SIAM J. Numer. Anal. 43 (4) (2005)
Bernardo Cockburn, Guido Kanschat, Dominik Schötzau
The local discontinuous Galerkin method for the Oseen equations. Math. Comput. 73 (246) (2004)
Bernardo Cockburn, Jayadeep Gopalakrishnan
A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems. SIAM J. Numer. Anal. 42 (1) (2004)
Bernardo Cockburn, Mitchell Luskin, Chi-Wang Shu, Endre Süli
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Math. Comput. 72 (242) (2003)
Samuel Albert, Bernardo Cockburn, Donald A. French, Todd E. Peterson
A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. Part I: The steady state case. Math. Comput. 71 (237) (2002)
Bernardo Cockburn, Guido Kanschat, Dominik Schötzau, Christoph Schwab
Local Discontinuous Galerkin Methods for the Stokes System. SIAM J. Numer. Anal. 40 (1) (2002)
Paul Castillo, Bernardo Cockburn, Dominik Schötzau, Christoph Schwab
Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems. Math. Comput. 71 (238) (2002)
Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn, L. Donatella Marini
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems. SIAM J. Numer. Anal. 39 (5) (2002)

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Publication Activity (10 Years)

Top Topics

Top Venues

Bernardo Cockburn