Bernardo Cockburn

Orcid: 0000-0001-6085-3441

Affiliations:
  • University of Minnesota, USA


According to our database1, Bernardo Cockburn authored at least 109 papers between 1993 and 2023.

Collaborative distances:
  • Dijkstra number2 of four.
  • Erdős number3 of four.

Timeline

Legend:

Book 
In proceedings 
Article 
PhD thesis 
Dataset
Other 

Links

Online presence:

On csauthors.net:

Bibliography

2023
Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems.
Frontiers Appl. Math. Stat., 2023

Efficient implementation of the hybridized Raviart-Thomas mixed method by converting flux subspaces into stabilizations.
CoRR, 2023

2022
An adjoint-based adaptive error approximation of functionals by the hybridizable discontinuous Galerkin method for second-order elliptic equations.
J. Comput. Phys., 2022

An adjoint-based super-convergent Galerkin approximation of eigenvalues.
J. Comput. Phys., 2022

Discontinuous Galerkin Methods with Time-Operators in Their Numerical Traces for Time-Dependent Electromagnetics.
Comput. Methods Appl. Math., 2022

2020
Superconvergent Interpolatory HDG methods for reaction diffusion equations II: HHO-inspired methods.
CoRR, 2020

2019
Interpolatory HDG Method for Parabolic Semilinear PDEs.
J. Sci. Comput., 2019

Superconvergent Interpolatory HDG Methods for Reaction Diffusion Equations I: An HDG<sub>k</sub> Method.
J. Sci. Comput., 2019

2018
Discrete H<sup>1</sup>-Inequalities for Spaces Admitting M-Decompositions.
SIAM J. Numer. Anal., 2018

Supercloseness of Primal-Dual Galerkin Approximations for Second Order Elliptic Problems.
J. Sci. Comput., 2018

Stormer-Numerov HDG Methods for Acoustic Waves.
J. Sci. Comput., 2018

2017
A Systematic Construction of Finite Element Commuting Exact Sequences.
SIAM J. Numer. Anal., 2017

Superconvergence by M-decompositions. Part I: General theory for HDG methods for diffusion.
Math. Comput., 2017

Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations.
Math. Comput., 2017

Adjoint-Based, Superconvergent Galerkin Approximations of Linear Functionals.
J. Sci. Comput., 2017

Symplectic Hamiltonian HDG methods for wave propagation phenomena.
J. Comput. Phys., 2017

2016
A Hybridizable Discontinuous Galerkin Method for the p-Laplacian.
SIAM J. Sci. Comput., 2016

Contraction property of adaptive hybridizable discontinuous Galerkin methods.
Math. Comput., 2016

Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces.
Math. Comput., 2016

Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension.
Math. Comput., 2016

The Staggered DG Method is the Limit of a Hybridizable DG Method. Part II: The Stokes Flow.
J. Sci. Comput., 2016

Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems.
Adv. Comput. Math., 2016

2015
A hybridizable discontinuous Galerkin method for fractional diffusion problems.
Numerische Mathematik, 2015

A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation.
J. Comput. Phys., 2015

A class of embedded discontinuous Galerkin methods for computational fluid dynamics.
J. Comput. Phys., 2015

2014
The Staggered DG Method is the Limit of a Hybridizable DG Method.
SIAM J. Numer. Anal., 2014

An a posteriori error estimate for the variable-degree Raviart-Thomas method.
Math. Comput., 2014

Divergence-conforming HDG methods for Stokes flows.
Math. Comput., 2014

A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity.
Math. Comput., 2014

Commuting diagrams for the TNT elements on cubes.
Math. Comput., 2014

Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation.
Math. Comput., 2014

Analysis of variable-degree HDG methods for Convection-Diffusion equations. Part II: Semimatching nonconforming meshes.
Math. Comput., 2014

Solving Convection-Diffusion Problems on Curved Domains by Extensions from Subdomains.
J. Sci. Comput., 2014

An adaptive spectral/DG method for a reduced phase-space based level set approach to geometrical optics on curved elements.
J. Comput. Phys., 2014

2013
A Posteriori Error Analysis for Hybridizable Discontinuous Galerkin Methods for Second Order Elliptic Problems.
SIAM J. Numer. Anal., 2013

Conditions for superconvergence of HDG methods for Stokes flow.
Math. Comput., 2013

Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations.
Math. Comput., 2013

Analysis of HDG Methods for Oseen Equations.
J. Sci. Comput., 2013

A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations.
J. Comput. Phys., 2013

2012
Coupling at a Distance HDG and BEM.
SIAM J. Sci. Comput., 2012

Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains.
SIAM J. Sci. Comput., 2012

Superconvergent HDG Methods on Isoparametric Elements for Second-Order Elliptic Problems.
SIAM J. Numer. Anal., 2012

Coupling of Raviart-Thomas and Hybridizable Discontinuous Galerkin Methods with BEM.
SIAM J. Numer. Anal., 2012

Conditions for superconvergence of HDG methods for second-order elliptic problems.
Math. Comput., 2012

An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions.
Math. Comput., 2012

Uniform-in-time superconvergence of HDG methods for the heat equation.
Math. Comput., 2012

A projection-based error analysis of HDG methods for Timoshenko beams.
Math. Comput., 2012

To CG or to HDG: A Comparative Study.
J. Sci. Comput., 2012

A Posteriori Error Estimates for HDG Methods.
J. Sci. Comput., 2012

Divergence-Free HDG Methods for the Vorticity-Velocity Formulation of the Stokes Problem.
J. Sci. Comput., 2012

A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains.
J. Comput. Phys., 2012

2011
Analysis of HDG methods for Stokes flow.
Math. Comput., 2011

Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations.
J. Comput. Phys., 2011

High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics.
J. Comput. Phys., 2011

An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations.
J. Comput. Phys., 2011

2010
Hybridization and Postprocessing Techniques for Mixed Eigenfunctions.
SIAM J. Numer. Anal., 2010

Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity.
SIAM J. Numer. Anal., 2010

A projection-based error analysis of HDG methods.
Math. Comput., 2010

A new elasticity element made for enforcing weak stress symmetry.
Math. Comput., 2010

A Comparison of HDG Methods for Stokes Flow.
J. Sci. Comput., 2010

Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains.
J. Sci. Comput., 2010

Hybridizable Discontinuous Galerkin Methods for Timoshenko Beams.
J. Sci. Comput., 2010

2009
A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems.
SIAM J. Sci. Comput., 2009

An Analysis of the Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems.
SIAM J. Numer. Anal., 2009

Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems.
SIAM J. Numer. Anal., 2009

The Derivation of Hybridizable Discontinuous Galerkin Methods for Stokes Flow.
SIAM J. Numer. Anal., 2009

Superconvergent discontinuous Galerkin methods for second-order elliptic problems.
Math. Comput., 2009

Foreword.
J. Sci. Comput., 2009

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations.
J. Sci. Comput., 2009

A Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems.
J. Sci. Comput., 2009

Local derivative post-processing for the discontinuous Galerkin method.
J. Comput. Phys., 2009

An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations.
J. Comput. Phys., 2009

An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations.
J. Comput. Phys., 2009

2008
Error Estimates for the Runge-Kutta Discontinuous Galerkin Method for the Transport Equation with Discontinuous Initial Data.
SIAM J. Numer. Anal., 2008

Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes.
SIAM J. Numer. Anal., 2008

A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems.
Math. Comput., 2008

The Computation of a Locally Conservative Stress for the Continuous Galerkin Method for Compressible Linearly Elastic Materials.
J. Sci. Comput., 2008

2007
Locally Conservative Fluxes for the Continuous Galerkin Method.
SIAM J. Numer. Anal., 2007

Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension.
Math. Comput., 2007

A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier-Stokes Equations.
J. Sci. Comput., 2007

Adjoint Recovery of Superconvergent Linear Functionals from Galerkin Approximations. The One-dimensional Case.
J. Sci. Comput., 2007

An Analysis of the Minimal Dissipation Local Discontinuous Galerkin Method for Convection-Diffusion Problems.
J. Sci. Comput., 2007

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., 2007

2006
Locking-Free Optimal Discontinuous Galerkin Methods for Timoshenko Beams.
SIAM J. Numer. Anal., 2006

Hybridized globally divergence-free LDG methods. Part I: The Stokes problem.
Math. Comput., 2006

Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Timoshenko Beams.
J. Sci. Comput., 2006

2005
Incompressible Finite Elements via Hybridization. Part II: The Stokes System in Three Space Dimensions.
SIAM J. Numer. Anal., 2005

Incompressible Finite Elements via Hybridization. Part I: The Stokes System in Two Space Dimensions.
SIAM J. Numer. Anal., 2005

A locally conservative LDG method for the incompressible Navier-Stokes equations.
Math. Comput., 2005

Error analysis of variable degree mixed methods for elliptic problems via hybridization.
Math. Comput., 2005

High-order RKDG Methods for Computational Electromagnetics.
J. Sci. Comput., 2005

An <i>A Posteriori</i> Error Estimate for the Local Discontinuous Galerkin Method Applied to Linear and Nonlinear Diffusion Problems.
J. Sci. Comput., 2005

A Mixed Finite Element Method for Elasticity in Three Dimensions.
J. Sci. Comput., 2005

2004
A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems.
SIAM J. Numer. Anal., 2004

The local discontinuous Galerkin method for the Oseen equations.
Math. Comput., 2004

2003
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations.
Math. Comput., 2003

2002
Local Discontinuous Galerkin Methods for the Stokes System.
SIAM J. Numer. Anal., 2002

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems.
SIAM J. Numer. Anal., 2002

Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems.
Math. Comput., 2002

A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. Part I: The steady state case.
Math. Comput., 2002

2001
Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids.
SIAM J. Numer. Anal., 2001

Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems.
J. Sci. Comput., 2001

2000
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems.
SIAM J. Numer. Anal., 2000

1997
Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems.
Math. Comput., 1997

A priori error estimates for numerical methods for scalar conservation laws. Part II : flux-splitting monotone schemes on irregular Cartesian grids.
Math. Comput., 1997

1996
A Model Numerical Scheme for the Propagation of phase Transitions in Solids.
SIAM J. Sci. Comput., 1996

A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach.
Math. Comput., 1996

1995
Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation.
VLSI Design, 1995

1993
Finite Element Computation of the Hydrodynamic Model of Semiconductor Devices.
Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, 1993


  Loading...