Bernardo Cockburn

112 papers Journal 111Unranked 1

Year	Rank	Type	Title / Venue / Authors
2025	J	`jnl`	Improved L CoRR Bernardo Cockburn, Alexandre Ern, Rekha Khot
2025	J	`jnl`	The discretizations of the derivative by the continuous Galerkin and the discontinuous Galerkin methods are exactly the same. CoRR Bernardo Cockburn
2025	J	`jnl`	Turbo Post-processing for Discontinuous Galerkin Methods: One-Dimensional Linear Transport. J. Sci. Comput. Bernardo Cockburn, Zubin Lal
2023	J	`jnl`	Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems. Frontiers Appl. Math. Stat. Bernardo Cockburn, Shukai Du, Manuel A. Sánchez
2023	J	`jnl`	Efficient implementation of the hybridized Raviart-Thomas mixed method by converting flux subspaces into stabilizations. CoRR Sreevatsa Anantharamu, Bernardo Cockburn
2022	J	`jnl`	An adjoint-based adaptive error approximation of functionals by the hybridizable discontinuous Galerkin method for second-order elliptic equations. J. Comput. Phys. Bernardo Cockburn, Shiqiang Xia
2022	J	`jnl`	An adjoint-based super-convergent Galerkin approximation of eigenvalues. J. Comput. Phys. Bernardo Cockburn, Shiqiang Xia
2022	J	`jnl`	Discontinuous Galerkin Methods with Time-Operators in Their Numerical Traces for Time-Dependent Electromagnetics. Comput. Methods Appl. Math. Bernardo Cockburn, Shukai Du, Manuel A. Sánchez
2020	J	`jnl`	Superconvergent Interpolatory HDG methods for reaction diffusion equations II: HHO-inspired methods. CoRR Gang Chen, Bernardo Cockburn, John R. Singler, Yangwen Zhang
2019	J	`jnl`	Interpolatory HDG Method for Parabolic Semilinear PDEs. J. Sci. Comput. Bernardo Cockburn, John R. Singler, Yangwen Zhang
2019	J	`jnl`	Superconvergent Interpolatory HDG Methods for Reaction Diffusion Equations I: An HDG J. Sci. Comput. Gang Chen, Bernardo Cockburn, John R. Singler, Yangwen Zhang
2018	J	`jnl`	Discrete H SIAM J. Numer. Anal. Bernardo Cockburn, Guosheng Fu, Weifeng Qiu
2018	J	`jnl`	Stormer-Numerov HDG Methods for Acoustic Waves. J. Sci. Comput. Bernardo Cockburn, Zhixing Fu, Allan Hungria, Liangyue Ji, Manuel A. Sánchez, Francisco-Javier Sayas
2018	J	`jnl`	Supercloseness of Primal-Dual Galerkin Approximations for Second Order Elliptic Problems. J. Sci. Comput. Bernardo Cockburn, Manuel A. Sánchez, Chunguang Xiong
2017	J	`jnl`	A Systematic Construction of Finite Element Commuting Exact Sequences. SIAM J. Numer. Anal. Bernardo Cockburn, Guosheng Fu
2017	J	`jnl`	Adjoint-Based, Superconvergent Galerkin Approximations of Linear Functionals. J. Sci. Comput. Bernardo Cockburn, Zhu Wang
2017	J	`jnl`	Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations. Math. Comput. Ayçil Çesmelioglu, Bernardo Cockburn, Weifeng Qiu
2017	J	`jnl`	Superconvergence by M-decompositions. Part I: General theory for HDG methods for diffusion. Math. Comput. Bernardo Cockburn, Guosheng Fu, Francisco-Javier Sayas
2017	J	`jnl`	Symplectic Hamiltonian HDG methods for wave propagation phenomena. J. Comput. Phys. Manuel A. Sánchez, C. Ciuca, Ngoc Cuong Nguyen, Jaime Peraire, Bernardo Cockburn
2016	J	`jnl`	A Hybridizable Discontinuous Galerkin Method for the p-Laplacian. SIAM J. Sci. Comput. Bernardo Cockburn, Jiguang Shen
2016	J	`jnl`	Contraction property of adaptive hybridizable discontinuous Galerkin methods. Math. Comput. Bernardo Cockburn, Ricardo H. Nochetto, Wujun Zhang
2016	J	`jnl`	Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems. Adv. Comput. Math. Kassem Mustapha, Maher Nour, Bernardo Cockburn
2016	J	`jnl`	Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces. Math. Comput. Bernardo Cockburn, Alan Demlow
2016	J	`jnl`	Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension. Math. Comput. Yanlai Chen, Bernardo Cockburn, Bo Dong
2016	J	`jnl`	The Staggered DG Method is the Limit of a Hybridizable DG Method. Part II: The Stokes Flow. J. Sci. Comput. Eric T. Chung, Bernardo Cockburn, Guosheng Fu
2015	J	`jnl`	A class of embedded discontinuous Galerkin methods for computational fluid dynamics. J. Comput. Phys. Ngoc Cuong Nguyen, Jaime Peraire, Bernardo Cockburn
2015	J	`jnl`	A hybridizable discontinuous Galerkin method for fractional diffusion problems. Numerische Mathematik Bernardo Cockburn, Kassem Mustapha
2015	J	`jnl`	A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation. J. Comput. Phys. Ngoc Cuong Nguyen, Jaime Peraire, Fernando Reitich, Bernardo Cockburn
2014	J	`jnl`	A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity. Math. Comput. Bernardo Cockburn, Weifeng Qiu, Manuel E. Solano
2014	J	`jnl`	An a posteriori error estimate for the variable-degree Raviart-Thomas method. Math. Comput. Bernardo Cockburn, Wujun Zhang
2014	J	`jnl`	An adaptive spectral/DG method for a reduced phase-space based level set approach to geometrical optics on curved elements. J. Comput. Phys. Bernardo Cockburn, Chiu-Yen Kao, Fernando Reitich
2014	J	`jnl`	Analysis of variable-degree HDG methods for Convection-Diffusion equations. Part II: Semimatching nonconforming meshes. Math. Comput. Yanlai Chen, Bernardo Cockburn
2014	J	`jnl`	Commuting diagrams for the TNT elements on cubes. Math. Comput. Bernardo Cockburn, Weifeng Qiu
2014	J	`jnl`	Divergence-conforming HDG methods for Stokes flows. Math. Comput. Bernardo Cockburn, Francisco-Javier Sayas
2014	J	`jnl`	Solving Convection-Diffusion Problems on Curved Domains by Extensions from Subdomains. J. Sci. Comput. Bernardo Cockburn, Manuel E. Solano
2014	J	`jnl`	The Staggered DG Method is the Limit of a Hybridizable DG Method. SIAM J. Numer. Anal. Eric T. Chung, Bernardo Cockburn, Guosheng Fu
2014	J	`jnl`	Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation. Math. Comput. Bernardo Cockburn, Vincent Quenneville-Bélair
2013	J	`jnl`	A Posteriori Error Analysis for Hybridizable Discontinuous Galerkin Methods for Second Order Elliptic Problems. SIAM J. Numer. Anal. Bernardo Cockburn, Wujun Zhang
2013	J	`jnl`	A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations. J. Comput. Phys. Sander Rhebergen, Bernardo Cockburn, Jaap J. W. van der Vegt
2013	J	`jnl`	Analysis of HDG Methods for Oseen Equations. J. Sci. Comput. Ayçil Çesmelioglu, Bernardo Cockburn, Ngoc Cuong Nguyen, Jaume Peraire
2013	J	`jnl`	Conditions for superconvergence of HDG methods for Stokes flow. Math. Comput. Bernardo Cockburn, Ke Shi
2013	J	`jnl`	Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations. Math. Comput. Bernardo Cockburn, Ivan Merev, Jianliang Qian
2012	J	`jnl`	A Posteriori Error Estimates for HDG Methods. J. Sci. Comput. Bernardo Cockburn, Wujun Zhang
2012	J	`jnl`	A projection-based error analysis of HDG methods for Timoshenko beams. Math. Comput. Fatih Celiker, Bernardo Cockburn, Ke Shi
2012	J	`jnl`	A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains. J. Comput. Phys. Sander Rhebergen, Bernardo Cockburn
2012	J	`jnl`	An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions. Math. Comput. Bernardo Cockburn, Jintao Cui
2012	J	`jnl`	Conditions for superconvergence of HDG methods for second-order elliptic problems. Math. Comput. Bernardo Cockburn, Weifeng Qiu, Ke Shi
2012	J	`jnl`	Coupling at a Distance HDG and BEM. SIAM J. Sci. Comput. Bernardo Cockburn, Francisco-Javier Sayas, Manuel E. Solano
2012	J	`jnl`	Coupling of Raviart-Thomas and Hybridizable Discontinuous Galerkin Methods with BEM. SIAM J. Numer. Anal. Bernardo Cockburn, Johnny Guzmán, Francisco-Javier Sayas
2012	J	`jnl`	Divergence-Free HDG Methods for the Vorticity-Velocity Formulation of the Stokes Problem. J. Sci. Comput. Bernardo Cockburn, Jintao Cui
2012	J	`jnl`	Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains. SIAM J. Sci. Comput. Bernardo Cockburn, Manuel E. Solano
2012	J	`jnl`	Superconvergent HDG Methods on Isoparametric Elements for Second-Order Elliptic Problems. SIAM J. Numer. Anal. Bernardo Cockburn, Weifeng Qiu, Ke Shi
2012	J	`jnl`	To CG or to HDG: A Comparative Study. J. Sci. Comput. Robert M. Kirby, Spencer J. Sherwin, Bernardo Cockburn
2012	J	`jnl`	Uniform-in-time superconvergence of HDG methods for the heat equation. Math. Comput. Brandon Chabaud, Bernardo Cockburn
2011	J	`jnl`	An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. J. Comput. Phys. Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn
2011	J	`jnl`	Analysis of HDG methods for Stokes flow. Math. Comput. Bernardo Cockburn, Jayadeep Gopalakrishnan, Ngoc Cuong Nguyen, Jaume Peraire, Francisco-Javier Sayas
2011	J	`jnl`	High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. J. Comput. Phys. Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn
2011	J	`jnl`	Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations. J. Comput. Phys. Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn
2010	J	`jnl`	A Comparison of HDG Methods for Stokes Flow. J. Sci. Comput. Bernardo Cockburn, Ngoc Cuong Nguyen, Jaume Peraire
2010	J	`jnl`	A new elasticity element made for enforcing weak stress symmetry. Math. Comput. Bernardo Cockburn, Jayadeep Gopalakrishnan, Johnny Guzmán
2010	J	`jnl`	A projection-based error analysis of HDG methods. Math. Comput. Bernardo Cockburn, Jayadeep Gopalakrishnan, Francisco-Javier Sayas
2010	J	`jnl`	Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains. J. Sci. Comput. Bernardo Cockburn, Deepa Gupta, Fernando Reitich
2010	J	`jnl`	Hybridizable Discontinuous Galerkin Methods for Timoshenko Beams. J. Sci. Comput. Fatih Celiker, Bernardo Cockburn, Ke Shi
2010	J	`jnl`	Hybridization and Postprocessing Techniques for Mixed Eigenfunctions. SIAM J. Numer. Anal. Bernardo Cockburn, Jayadeep Gopalakrishnan, F. Li, Ngoc Cuong Nguyen, Jaume Peraire
2010	J	`jnl`	Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity. SIAM J. Numer. Anal. Bernardo Cockburn, Bo Dong, Johnny Guzmán, Jianliang Qian
2009	J	`jnl`	A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems. SIAM J. Sci. Comput. Bernardo Cockburn, Bo Dong, Johnny Guzmán, Marco Restelli, Riccardo Sacco
2009	J	`jnl`	A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems. J. Sci. Comput. Bernardo Cockburn, Bo Dong, Johnny Guzmán
2009	J	`jnl`	An Analysis of the Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems. SIAM J. Numer. Anal. Bernardo Cockburn, Johnny Guzmán, See-Chew Soon, Henry K. Stolarski
2009	J	`jnl`	An Equal-Order DG Method for the Incompressible Navier-Stokes Equations. J. Sci. Comput. Bernardo Cockburn, Guido Kanschat, Dominik Schötzau
2009	J	`jnl`	An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. J. Comput. Phys. Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn
2009	J	`jnl`	An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. J. Comput. Phys. Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn
2009	J	`jnl`	Foreword. J. Sci. Comput. Bernardo Cockburn, Chi-Wang Shu
2009	J	`jnl`	Local derivative post-processing for the discontinuous Galerkin method. J. Comput. Phys. Jennifer K. Ryan, Bernardo Cockburn
2009	J	`jnl`	Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Math. Comput. Bernardo Cockburn, Johnny Guzmán, Haiying Wang
2009	J	`jnl`	The Derivation of Hybridizable Discontinuous Galerkin Methods for Stokes Flow. SIAM J. Numer. Anal. Bernardo Cockburn, Jayadeep Gopalakrishnan
2009	J	`jnl`	Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems. SIAM J. Numer. Anal. Bernardo Cockburn, Jayadeep Gopalakrishnan, Raytcho D. Lazarov
2008	J	`jnl`	A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Math. Comput. Bernardo Cockburn, Bo Dong, Johnny Guzmán
2008	J	`jnl`	Error Estimates for the Runge-Kutta Discontinuous Galerkin Method for the Transport Equation with Discontinuous Initial Data. SIAM J. Numer. Anal. Bernardo Cockburn, Johnny Guzmán
2008	J	`jnl`	Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes. SIAM J. Numer. Anal. Bernardo Cockburn, Bo Dong, Johnny Guzmán
2008	J	`jnl`	The Computation of a Locally Conservative Stress for the Continuous Galerkin Method for Compressible Linearly Elastic Materials. J. Sci. Comput. Bernardo Cockburn, Haiying Wang
2007	J	`jnl`	A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier-Stokes Equations. J. Sci. Comput. Bernardo Cockburn, Guido Kanschat, Dominik Schötzau
2007	J	`jnl`	Adjoint Recovery of Superconvergent Linear Functionals from Galerkin Approximations. The One-dimensional Case. J. Sci. Comput. Bernardo Cockburn, Ryuhei Ichikawa
2007	J	`jnl`	An Analysis of the Minimal Dissipation Local Discontinuous Galerkin Method for Convection-Diffusion Problems. J. Sci. Comput. Bernardo Cockburn, Bo Dong
2007	J	`jnl`	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. Yanlai Chen, Bernardo Cockburn
2007	J	`jnl`	Locally Conservative Fluxes for the Continuous Galerkin Method. SIAM J. Numer. Anal. Bernardo Cockburn, Jayadeep Gopalakrishnan, Haiying Wang
2007	J	`jnl`	Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension. Math. Comput. Fatih Celiker, Bernardo Cockburn
2006	J	`jnl`	Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Timoshenko Beams. J. Sci. Comput. Fatih Celiker, Bernardo Cockburn
2006	J	`jnl`	Hybridized globally divergence-free LDG methods. Part I: The Stokes problem. Math. Comput. Jesús Carrero, Bernardo Cockburn, Dominik Schötzau
2006	J	`jnl`	Locking-Free Optimal Discontinuous Galerkin Methods for Timoshenko Beams. SIAM J. Numer. Anal. Fatih Celiker, Bernardo Cockburn, Henry K. Stolarski
2005	J	`jnl`	A Mixed Finite Element Method for Elasticity in Three Dimensions. J. Sci. Comput. Scot Adams, Bernardo Cockburn
2005	J	`jnl`	A locally conservative LDG method for the incompressible Navier-Stokes equations. Math. Comput. Bernardo Cockburn, Guido Kanschat, Dominik Schötzau
2005	J	`jnl`	An J. Sci. Comput. Rommel Bustinza, Gabriel N. Gatica, Bernardo Cockburn
2005	J	`jnl`	Error analysis of variable degree mixed methods for elliptic problems via hybridization. Math. Comput. Bernardo Cockburn, Jayadeep Gopalakrishnan
2005	J	`jnl`	High-order RKDG Methods for Computational Electromagnetics. J. Sci. Comput. Min-Hung Chen, Bernardo Cockburn, Fernando Reitich
2005	J	`jnl`	Incompressible Finite Elements via Hybridization. Part I: The Stokes System in Two Space Dimensions. SIAM J. Numer. Anal. Bernardo Cockburn, Jayadeep Gopalakrishnan
2005	J	`jnl`	Incompressible Finite Elements via Hybridization. Part II: The Stokes System in Three Space Dimensions. SIAM J. Numer. Anal. Bernardo Cockburn, Jayadeep Gopalakrishnan
2004	J	`jnl`	A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems. SIAM J. Numer. Anal. Bernardo Cockburn, Jayadeep Gopalakrishnan
2004	J	`jnl`	The local discontinuous Galerkin method for the Oseen equations. Math. Comput. Bernardo Cockburn, Guido Kanschat, Dominik Schötzau
2003	J	`jnl`	Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Math. Comput. Bernardo Cockburn, Mitchell Luskin, Chi-Wang Shu, Endre Süli
2002	J	`jnl`	A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. Part I: The steady state case. Math. Comput. Samuel Albert, Bernardo Cockburn, Donald A. French, Todd E. Peterson
2002	J	`jnl`	Local Discontinuous Galerkin Methods for the Stokes System. SIAM J. Numer. Anal. Bernardo Cockburn, Guido Kanschat, Dominik Schötzau, Christoph Schwab
2002	J	`jnl`	Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems. Math. Comput. Paul Castillo, Bernardo Cockburn, Dominik Schötzau, Christoph Schwab
2002	J	`jnl`	Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems. SIAM J. Numer. Anal. Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn, L. Donatella Marini
2001	J	`jnl`	Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems. J. Sci. Comput. Bernardo Cockburn, Chi-Wang Shu
2001	J	`jnl`	Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids. SIAM J. Numer. Anal. Bernardo Cockburn, Guido Kanschat, Ilaria Perugia, Dominik Schötzau
2000	J	`jnl`	An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems. SIAM J. Numer. Anal. Paul Castillo, Bernardo Cockburn, Ilaria Perugia, Dominik Schötzau
1997	J	`jnl`	A priori error estimates for numerical methods for scalar conservation laws. Part II : flux-splitting monotone schemes on irregular Cartesian grids. Math. Comput. Bernardo Cockburn, Pierre-Alain Gremaud
1997	J	`jnl`	Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems. Math. Comput. Bernardo Cockburn, Don A. Jones, Edriss S. Titi
1996	J	`jnl`	A Model Numerical Scheme for the Propagation of phase Transitions in Solids. SIAM J. Sci. Comput. Bernardo Cockburn, Huiing Gau
1996	J	`jnl`	A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach. Math. Comput. Bernardo Cockburn, Pierre-Alain Gremaud
1995	J	`jnl`	Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation. VLSI Design Zhangxin Chen, Bernardo Cockburn, Joseph W. Jerome, Chi-Wang Shu
1993	—	`conf`	Finite Element Computation of the Hydrodynamic Model of Semiconductor Devices. PPSC Zhangxin Chen, Bernardo Cockburn, Joseph W. Jerome, Chi-Wang Shu