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Mathematics
USA
2026

D-Index & Metrics

Mathematics

D-Index
81
Citations
42379
World Ranking
132
National Ranking
75

Research.com Recognitions

  • 2026 - Research.com Mathematics in United States Leader Award
  • 2025 - Research.com Mathematics in United States Leader Award

Overview

Bernardo Cockburn is affiliated with the University of Minnesota in the United States. Their research spans several interconnected fields primarily within engineering and mathematics, with a focus on advanced numerical methods and computational mathematics.

The main fields of study for Cockburn include:

  • Engineering
  • Mathematics

Within these broader areas, Cockburn's work concentrates on subfields such as:

  • Computational Mechanics
  • Numerical Analysis
  • Electrical and Electronic Engineering
  • Computational Theory and Mathematics
  • Mechanics of Materials

The scientist's research topics cover a variety of specialized domains, including:

  • Advanced Numerical Methods in Computational Mathematics
  • Numerical methods for differential equations
  • Electromagnetic Simulation and Numerical Methods
  • Advanced Mathematical Modeling in Engineering
  • Numerical methods in engineering
  • Differential Equations and Numerical Methods
  • Computational Fluid Dynamics and Aerodynamics

Bernardo Cockburn has a publication record that includes notable recent papers such as:

  • Hybridizable discontinuous Galerkin methods for second-order elliptic problems: overview, a new result and open problems (2023), published in Japan Journal of Industrial and Applied Mathematics
  • The pursuit of a dream, Francisco Javier Sayas and the HDG methods (2021), published in SeMA Journal

While Cockburn has collaborated closely with several researchers, frequent coauthors include:

  • Manuel A. Sánchez
  • Shukai Du
  • Shiqiang Xia
  • Ngoc Cuong Nguyen
  • J. Peraire

Some of the preferred venues for publishing Cockburn's work are:

  • arXiv (Cornell University)
  • Computer Methods in Applied Mechanics and Engineering
  • Journal of Computational Physics
  • IMA Journal of Numerical Analysis
  • Japan Journal of Industrial and Applied Mathematics

Best Publications

  • Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

    Douglas N. Arnold;Franco Brezzi;Bernardo Cockburn;L. Donatella Marini

  • The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V

    Bernardo Cockburn;Chi-Wang Shu

  • The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

    Bernardo Cockburn;Chi-Wang Shu

  • TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework

    Bernardo Cockburn;Chi Wang Shu

  • The Development of Discontinuous Galerkin Methods

    Bernardo Cockburn;George E. Karniadakis;Chi-Wang Shu

  • Runge-Kutta discontinuous Galerkin methods for convection-dominated problems

    Bernardo Cockburn;Chi-Wang Shu

  • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems

    B. Cockburn;S.-Y. Lin;C.-W. Shu

  • The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case

    Bernardo Cockburn;Bernardo Cockburn;Suchung Hou;Suchung Hou;Chi Wang Shu;Chi Wang Shu

  • Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems

    Bernardo Cockburn;Jayadeep Gopalakrishnan;Raytcho Lazarov

  • Discontinuous Galerkin Methods: Theory, Computation and Applications

    Bernardo Cockburn;George E. Karniadakis;Chi-Wang Shu

  • The Runge-Kutta local projection $P^1$ -discontinuous-Galerkin finite element method for scalar conservation laws

    Bernardo Cockburn;Chi-Wang Shu

  • Discontinuous Galerkin methods

    Bernardo Cockburn

  • An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems

    Paul Castillo;Bernardo Cockburn

  • Discontinuous Galerkin Methods for Convection-Dominated Problems

    Bernardo Cockburn

  • A locally conservative LDG method for the incompressible Navier-Stokes equations

    Bernardo Cockburn;Guido Kanschat;Dominik Schötzau

  • An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations

    N. C. Nguyen;J. Peraire;B. Cockburn

  • Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids

    Bernardo Cockburn;Guido Kanschat;Ilaria Perugia;Dominik Schötzau

  • Locally divergence-free discontinuous Galerkin methods for the Maxwell equations

    Bernardo Cockburn;Fengyan Li;Chi-Wang Shu

  • Advanced Numerical Approximation of Nonlinear Hyperbolic Equations

    Unknown

  • Local Discontinuous Galerkin Methods for the Stokes System

    Bernardo Cockburn;Guido Kanschat;Dominik Schötzau;Christoph Schwab

  • An introduction to the Discontinuous Galerkin method for convection-dominated problems

    Bernardo Cockburn

Frequent Co-Authors

Chi-Wang Shu
Chi-Wang Shu Brown University
Dominik Schötzau
Dominik Schötzau University of British Columbia
Johnny Guzmán
Johnny Guzmán Brown University
Zhangxin Chen
Zhangxin Chen University of Calgary
Eric T. Chung
Eric T. Chung Chinese University of Hong Kong
Endre Süli
Endre Süli University of Oxford
Clint Dawson
Clint Dawson The University of Texas at Austin
Franco Brezzi
Franco Brezzi National Research Council (CNR)
Patrick Joly
Patrick Joly École Nationale Supérieure de Techniques Avancées

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