Finite Element Computation of the Hydrodynamic Model of Semiconductor Devices. - Zhangxin Chen; Bernardo Cockburn; Joseph W. Jerome; Chi-Wang Shu (PPSC, 1993)

Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation. - Zhangxin Chen; Bernardo Cockburn; Joseph W. Jerome; Chi-Wang Shu (VLSI Design, 1995)

A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach. - Bernardo Cockburn; Pierre-Alain Gremaud (Math. Comput., 1996)

A Model Numerical Scheme for the Propagation of phase Transitions in Solids. - Bernardo Cockburn; Huiing Gau (SIAM J. Sci. Comput., 1996)

A priori error estimates for numerical methods for scalar conservation laws. Part II : flux-splitting monotone schemes on irregular Cartesian grids. - Bernardo Cockburn; Pierre-Alain Gremaud (Math. Comput., 1997)

Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems. - Bernardo Cockburn; Don A. Jones; Edriss S. Titi (Math. Comput., 1997)

An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems. - Paul Castillo 001; Bernardo Cockburn; Ilaria Perugia; Dominik Schötzau (SIAM J. Numer. Anal., 2000)

Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems. - Bernardo Cockburn; Chi-Wang Shu (J. Sci. Comput., 2001)

Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids. - Bernardo Cockburn; Guido Kanschat; Ilaria Perugia; Dominik Schötzau (SIAM J. Numer. Anal., 2001)

A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. Part I: The steady state case. - Samuel Albert; Bernardo Cockburn; Donald A. French; Todd E. Peterson 001 (Math. Comput., 2002)

Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems. - Paul Castillo 001; Bernardo Cockburn; Dominik Schötzau; Christoph Schwab (Math. Comput., 2002)

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems. - Douglas N. Arnold; Franco Brezzi; Bernardo Cockburn; L. Donatella Marini (SIAM J. Numer. Anal., 2002)

Local Discontinuous Galerkin Methods for the Stokes System. - Bernardo Cockburn; Guido Kanschat; Dominik Schötzau; Christoph Schwab (SIAM J. Numer. Anal., 2002)

Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. - Bernardo Cockburn; Mitchell Luskin; Chi-Wang Shu; Endre Süli (Math. Comput., 2003)

The local discontinuous Galerkin method for the Oseen equations. - Bernardo Cockburn; Guido Kanschat; Dominik Schötzau (Math. Comput., 2004)

A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems. - Bernardo Cockburn; Jayadeep Gopalakrishnan (SIAM J. Numer. Anal., 2004)

A Mixed Finite Element Method for Elasticity in Three Dimensions. - Scot Adams; Bernardo Cockburn (J. Sci. Comput., 2005)

An A Posteriori Error Estimate for the Local Discontinuous Galerkin Method Applied to Linear and Nonlinear Diffusion Problems. - Rommel Bustinza; Gabriel N. Gatica; Bernardo Cockburn (J. Sci. Comput., 2005)

High-order RKDG Methods for Computational Electromagnetics. - Min-Hung Chen; Bernardo Cockburn; Fernando Reitich (J. Sci. Comput., 2005)

Error analysis of variable degree mixed methods for elliptic problems via hybridization. - Bernardo Cockburn; Jayadeep Gopalakrishnan (Math. Comput., 2005)

A locally conservative LDG method for the incompressible Navier-Stokes equations. - Bernardo Cockburn; Guido Kanschat; Dominik Schötzau (Math. Comput., 2005)

Incompressible Finite Elements via Hybridization. Part I: The Stokes System in Two Space Dimensions. - Bernardo Cockburn; Jayadeep Gopalakrishnan (SIAM J. Numer. Anal., 2005)

Incompressible Finite Elements via Hybridization. Part II: The Stokes System in Three Space Dimensions. - Bernardo Cockburn; Jayadeep Gopalakrishnan (SIAM J. Numer. Anal., 2005)

Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Timoshenko Beams. - Fatih Celiker; Bernardo Cockburn (J. Sci. Comput., 2006)

Hybridized globally divergence-free LDG methods. Part I: The Stokes problem. - Jesús Carrero; Bernardo Cockburn; Dominik Schötzau (Math. Comput., 2006)

Locking-Free Optimal Discontinuous Galerkin Methods for Timoshenko Beams. - Fatih Celiker; Bernardo Cockburn; Henry K. Stolarski (SIAM J. Numer. Anal., 2006)

An adaptive high-order discontinuous Galerkin method with error control for the Hamilton-Jacobi equations. Part I: The one-dimensional steady state case. - Yanlai Chen; Bernardo Cockburn (J. Comput. Phys., 2007)

An Analysis of the Minimal Dissipation Local Discontinuous Galerkin Method for Convection-Diffusion Problems. - Bernardo Cockburn; Bo Dong (J. Sci. Comput., 2007)

Adjoint Recovery of Superconvergent Linear Functionals from Galerkin Approximations. The One-dimensional Case. - Bernardo Cockburn; Ryuhei Ichikawa (J. Sci. Comput., 2007)

A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier-Stokes Equations. - Bernardo Cockburn; Guido Kanschat; Dominik Schötzau (J. Sci. Comput., 2007)

Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension. - Fatih Celiker; Bernardo Cockburn (Math. Comput., 2007)

Locally Conservative Fluxes for the Continuous Galerkin Method. - Bernardo Cockburn; Jayadeep Gopalakrishnan; Haiying Wang 009 (SIAM J. Numer. Anal., 2007)

The Computation of a Locally Conservative Stress for the Continuous Galerkin Method for Compressible Linearly Elastic Materials. - Bernardo Cockburn; Haiying Wang 009 (J. Sci. Comput., 2008)

A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. - Bernardo Cockburn; Bo Dong; Johnny Guzmán (Math. Comput., 2008)

Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes. - Bernardo Cockburn; Bo Dong; Johnny Guzmán (SIAM J. Numer. Anal., 2008)

Error Estimates for the Runge-Kutta Discontinuous Galerkin Method for the Transport Equation with Discontinuous Initial Data. - Bernardo Cockburn; Johnny Guzmán (SIAM J. Numer. Anal., 2008)

An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. - Ngoc Cuong Nguyen; Jaume Peraire; Bernardo Cockburn (J. Comput. Phys., 2009)

An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. - Ngoc Cuong Nguyen; Jaume Peraire; Bernardo Cockburn (J. Comput. Phys., 2009)

Local derivative post-processing for the discontinuous Galerkin method. - Jennifer K. Ryan; Bernardo Cockburn (J. Comput. Phys., 2009)

A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems. - Bernardo Cockburn; Bo Dong; Johnny Guzmán (J. Sci. Comput., 2009)

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations. - Bernardo Cockburn; Guido Kanschat; Dominik Schötzau (J. Sci. Comput., 2009)

Foreword. - Bernardo Cockburn; Chi-Wang Shu (J. Sci. Comput., 2009)

Superconvergent discontinuous Galerkin methods for second-order elliptic problems. - Bernardo Cockburn; Johnny Guzmán; Haiying Wang 009 (Math. Comput., 2009)

The Derivation of Hybridizable Discontinuous Galerkin Methods for Stokes Flow. - Bernardo Cockburn; Jayadeep Gopalakrishnan (SIAM J. Numer. Anal., 2009)

Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems. - Bernardo Cockburn; Jayadeep Gopalakrishnan; Raytcho D. Lazarov (SIAM J. Numer. Anal., 2009)

An Analysis of the Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems. - Bernardo Cockburn; Johnny Guzmán; See-Chew Soon; Henry K. Stolarski (SIAM J. Numer. Anal., 2009)

A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems. - Bernardo Cockburn; Bo Dong; Johnny Guzmán; Marco Restelli; Riccardo Sacco (SIAM J. Sci. Comput., 2009)

Hybridizable Discontinuous Galerkin Methods for Timoshenko Beams. - Fatih Celiker; Bernardo Cockburn; Ke Shi 005 (J. Sci. Comput., 2010)

Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains. - Bernardo Cockburn; Deepa Gupta; Fernando Reitich (J. Sci. Comput., 2010)

A Comparison of HDG Methods for Stokes Flow. - Bernardo Cockburn; Ngoc Cuong Nguyen; Jaume Peraire (J. Sci. Comput., 2010)

A new elasticity element made for enforcing weak stress symmetry. - Bernardo Cockburn; Jayadeep Gopalakrishnan; Johnny Guzmán (Math. Comput., 2010)

A projection-based error analysis of HDG methods. - Bernardo Cockburn; Jayadeep Gopalakrishnan; Francisco-Javier Sayas (Math. Comput., 2010)

Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity. - Bernardo Cockburn; Bo Dong; Johnny Guzmán; Jianliang Qian (SIAM J. Numer. Anal., 2010)

Hybridization and Postprocessing Techniques for Mixed Eigenfunctions. - Bernardo Cockburn; Jayadeep Gopalakrishnan; F. Li; Ngoc Cuong Nguyen; Jaume Peraire (SIAM J. Numer. Anal., 2010)

An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. - Ngoc Cuong Nguyen; Jaume Peraire; Bernardo Cockburn (J. Comput. Phys., 2011)

High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. - Ngoc Cuong Nguyen; Jaume Peraire; Bernardo Cockburn (J. Comput. Phys., 2011)

Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations. - Ngoc Cuong Nguyen; Jaume Peraire; Bernardo Cockburn (J. Comput. Phys., 2011)

Analysis of HDG methods for Stokes flow. - Bernardo Cockburn; Jayadeep Gopalakrishnan; Ngoc Cuong Nguyen; Jaume Peraire; Francisco-Javier Sayas (Math. Comput., 2011)

A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. - Sander Rhebergen; Bernardo Cockburn (J. Comput. Phys., 2012)

Divergence-Free HDG Methods for the Vorticity-Velocity Formulation of the Stokes Problem. - Bernardo Cockburn; Jintao Cui (J. Sci. Comput., 2012)

A Posteriori Error Estimates for HDG Methods. - Bernardo Cockburn; Wujun Zhang (J. Sci. Comput., 2012)

To CG or to HDG: A Comparative Study. - Robert M. Kirby; Spencer J. Sherwin; Bernardo Cockburn (J. Sci. Comput., 2012)

A projection-based error analysis of HDG methods for Timoshenko beams. - Fatih Celiker; Bernardo Cockburn; Ke Shi 005 (Math. Comput., 2012)

Uniform-in-time superconvergence of HDG methods for the heat equation. - Brandon Chabaud; Bernardo Cockburn (Math. Comput., 2012)

An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions. - Bernardo Cockburn; Jintao Cui (Math. Comput., 2012)

Conditions for superconvergence of HDG methods for second-order elliptic problems. - Bernardo Cockburn; Weifeng Qiu; Ke Shi 005 (Math. Comput., 2012)

Coupling of Raviart-Thomas and Hybridizable Discontinuous Galerkin Methods with BEM. - Bernardo Cockburn; Johnny Guzmán; Francisco-Javier Sayas (SIAM J. Numer. Anal., 2012)

Superconvergent HDG Methods on Isoparametric Elements for Second-Order Elliptic Problems. - Bernardo Cockburn; Weifeng Qiu; Ke Shi 005 (SIAM J. Numer. Anal., 2012)

Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains. - Bernardo Cockburn; Manuel E. Solano (SIAM J. Sci. Comput., 2012)

Coupling at a Distance HDG and BEM. - Bernardo Cockburn; Francisco-Javier Sayas; Manuel E. Solano (SIAM J. Sci. Comput., 2012)

A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations. - Sander Rhebergen; Bernardo Cockburn; Jaap J. W. van der Vegt (J. Comput. Phys., 2013)

Analysis of HDG Methods for Oseen Equations. - Ayçil Çesmelioglu; Bernardo Cockburn; Ngoc Cuong Nguyen; Jaume Peraire (J. Sci. Comput., 2013)

Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations. - Bernardo Cockburn; Ivan Merev; Jianliang Qian (Math. Comput., 2013)

Conditions for superconvergence of HDG methods for Stokes flow. - Bernardo Cockburn; Ke Shi 005 (Math. Comput., 2013)

A Posteriori Error Analysis for Hybridizable Discontinuous Galerkin Methods for Second Order Elliptic Problems. - Bernardo Cockburn; Wujun Zhang (SIAM J. Numer. Anal., 2013)

An adaptive spectral/DG method for a reduced phase-space based level set approach to geometrical optics on curved elements. - Bernardo Cockburn; Chiu-Yen Kao; Fernando Reitich (J. Comput. Phys., 2014)

Solving Convection-Diffusion Problems on Curved Domains by Extensions from Subdomains. - Bernardo Cockburn; Manuel E. Solano (J. Sci. Comput., 2014)

Analysis of variable-degree HDG methods for Convection-Diffusion equations. Part II: Semimatching nonconforming meshes. - Yanlai Chen; Bernardo Cockburn (Math. Comput., 2014)

Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. - Bernardo Cockburn; Vincent Quenneville-Bélair (Math. Comput., 2014)

Commuting diagrams for the TNT elements on cubes. - Bernardo Cockburn; Weifeng Qiu (Math. Comput., 2014)

A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity. - Bernardo Cockburn; Weifeng Qiu; Manuel E. Solano (Math. Comput., 2014)

Divergence-conforming HDG methods for Stokes flows. - Bernardo Cockburn; Francisco-Javier Sayas (Math. Comput., 2014)

An a posteriori error estimate for the variable-degree Raviart-Thomas method. - Bernardo Cockburn; Wujun Zhang (Math. Comput., 2014)

The Staggered DG Method is the Limit of a Hybridizable DG Method. - Eric T. Chung 001; Bernardo Cockburn; Guosheng Fu (SIAM J. Numer. Anal., 2014)

A class of embedded discontinuous Galerkin methods for computational fluid dynamics. - Ngoc Cuong Nguyen; Jaime Peraire; Bernardo Cockburn (J. Comput. Phys., 2015)

A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation. - Ngoc Cuong Nguyen; Jaime Peraire; Fernando Reitich; Bernardo Cockburn (J. Comput. Phys., 2015)

A hybridizable discontinuous Galerkin method for fractional diffusion problems. - Bernardo Cockburn; Kassem Mustapha 001 (Numerische Mathematik, 2015)

Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems. - Kassem Mustapha 001; Maher Nour; Bernardo Cockburn (Adv. Comput. Math., 2016)

The Staggered DG Method is the Limit of a Hybridizable DG Method. Part II: The Stokes Flow. - Eric T. Chung 001; Bernardo Cockburn; Guosheng Fu (J. Sci. Comput., 2016)

Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension. - Yanlai Chen; Bernardo Cockburn; Bo Dong (Math. Comput., 2016)

Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces. - Bernardo Cockburn; Alan Demlow (Math. Comput., 2016)

Contraction property of adaptive hybridizable discontinuous Galerkin methods. - Bernardo Cockburn; Ricardo H. Nochetto; Wujun Zhang (Math. Comput., 2016)

A Hybridizable Discontinuous Galerkin Method for the p-Laplacian. - Bernardo Cockburn; Jiguang Shen (SIAM J. Sci. Comput., 2016)

Symplectic Hamiltonian HDG methods for wave propagation phenomena. - Manuel A. Sánchez; C. Ciuca; Ngoc Cuong Nguyen; Jaime Peraire; Bernardo Cockburn (J. Comput. Phys., 2017)

Adjoint-Based, Superconvergent Galerkin Approximations of Linear Functionals. - Bernardo Cockburn; Zhu Wang 003 (J. Sci. Comput., 2017)

Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations. - Ayçil Çesmelioglu; Bernardo Cockburn; Weifeng Qiu (Math. Comput., 2017)

Superconvergence by M-decompositions. Part I: General theory for HDG methods for diffusion. - Bernardo Cockburn; Guosheng Fu; Francisco-Javier Sayas (Math. Comput., 2017)

A Systematic Construction of Finite Element Commuting Exact Sequences. - Bernardo Cockburn; Guosheng Fu (SIAM J. Numer. Anal., 2017)

Stormer-Numerov HDG Methods for Acoustic Waves. - Bernardo Cockburn; Zhixing Fu; Allan Hungria; Liangyue Ji; Manuel A. Sánchez; Francisco-Javier Sayas (J. Sci. Comput., 2018)

Supercloseness of Primal-Dual Galerkin Approximations for Second Order Elliptic Problems. - Bernardo Cockburn; Manuel A. Sánchez; Chunguang Xiong (J. Sci. Comput., 2018)

Discrete H1-Inequalities for Spaces Admitting M-Decompositions. - Bernardo Cockburn; Guosheng Fu; Weifeng Qiu (SIAM J. Numer. Anal., 2018)

Superconvergent Interpolatory HDG Methods for Reaction Diffusion Equations I: An HDGk Method. - Gang Chen 025; Bernardo Cockburn; John R. Singler; Yangwen Zhang (J. Sci. Comput., 2019)

Interpolatory HDG Method for Parabolic Semilinear PDEs. - Bernardo Cockburn; John R. Singler; Yangwen Zhang (J. Sci. Comput., 2019)

Superconvergent Interpolatory HDG methods for reaction diffusion equations II: HHO-inspired methods. - Gang Chen 025; Bernardo Cockburn; John R. Singler; Yangwen Zhang (CoRR, 2020)

Discontinuous Galerkin Methods with Time-Operators in Their Numerical Traces for Time-Dependent Electromagnetics. - Bernardo Cockburn; Shukai Du; Manuel A. Sánchez (Comput. Methods Appl. Math., 2022)

An adjoint-based super-convergent Galerkin approximation of eigenvalues. - Bernardo Cockburn; Shiqiang Xia (J. Comput. Phys., 2022)

An adjoint-based adaptive error approximation of functionals by the hybridizable discontinuous Galerkin method for second-order elliptic equations. - Bernardo Cockburn; Shiqiang Xia (J. Comput. Phys., 2022)

Efficient implementation of the hybridized Raviart-Thomas mixed method by converting flux subspaces into stabilizations. - Sreevatsa Anantharamu; Bernardo Cockburn (CoRR, 2023)

Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems. - Bernardo Cockburn; Shukai Du; Manuel A. Sánchez (Frontiers Appl. Math. Stat., 2023)

Turbo Post-processing for Discontinuous Galerkin Methods: One-Dimensional Linear Transport. - Bernardo Cockburn; Zubin Lal (J. Sci. Comput., 2025)