Bernardo Cockburn

32.7k total citations · 12 hit papers
203 papers, 22.2k citations indexed

About

Bernardo Cockburn is a scholar working on Computational Mechanics, Numerical Analysis and Electrical and Electronic Engineering. According to data from OpenAlex, Bernardo Cockburn has authored 203 papers receiving a total of 22.2k indexed citations (citations by other indexed papers that have themselves been cited), including 187 papers in Computational Mechanics, 71 papers in Numerical Analysis and 61 papers in Electrical and Electronic Engineering. Recurrent topics in Bernardo Cockburn's work include Advanced Numerical Methods in Computational Mathematics (170 papers), Computational Fluid Dynamics and Aerodynamics (84 papers) and Electromagnetic Simulation and Numerical Methods (61 papers). Bernardo Cockburn is often cited by papers focused on Advanced Numerical Methods in Computational Mathematics (170 papers), Computational Fluid Dynamics and Aerodynamics (84 papers) and Electromagnetic Simulation and Numerical Methods (61 papers). Bernardo Cockburn collaborates with scholars based in United States, Germany and Chile. Bernardo Cockburn's co-authors include Chi‐Wang Shu, L. D. Marini, Franco Brezzi, Douglas N. Arnold, Jay Gopalakrishnan, Dominik Schötzau, Ngoc Cuong Nguyen, J. Peraire, San‐Yih Lin and Guido Kanschat and has published in prestigious journals such as Journal of Computational Physics, Computer Methods in Applied Mechanics and Engineering and Mathematics of Computation.

In The Last Decade

Bernardo Cockburn

197 papers receiving 20.7k citations

Hit Papers

5 papers align trajectories

What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

2002 2.3k citations Bernardo Cockburn et al. profile →
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

1998 1.8k citations Bernardo Cockburn, Chi‐Wang Shu profile →
The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V

1998 1.6k citations Bernardo Cockburn, Chi‐Wang Shu Journal of Computational Physics profile →
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework

1989 1.5k citations Bernardo Cockburn, Chi‐Wang Shu Mathematics of Computation profile →
TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems

1989 1.1k citations Bernardo Cockburn, Chi‐Wang Shu et al. Journal of Computational Physics profile →
The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case

1990 1.1k citations Bernardo Cockburn, Chi‐Wang Shu et al. Mathematics of Computation profile →
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems

2001 946 citations Bernardo Cockburn, Chi‐Wang Shu profile →
Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems

2009 764 citations Bernardo Cockburn, Jay Gopalakrishnan et al. profile →
The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws

1991 468 citations Bernardo Cockburn, Chi‐Wang Shu profile →
Discontinuous Galerkin Methods: Theory, Computation and Applications

2011 415 citations Bernardo Cockburn, George Em Karniadakis et al. CERN Document Server (European Organization for Nuclear Research) profile →
The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case

1990 383 citations Bernardo Cockburn, Chi‐Wang Shu et al. Mathematics of Computation profile →
TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework

1989 366 citations Bernardo Cockburn, Chi‐Wang Shu Mathematics of Computation profile →

Peers

Countries citing papers authored by Bernardo Cockburn

Since Specialization

Citations

This map shows the geographic impact of Bernardo Cockburn's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Bernardo Cockburn with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Bernardo Cockburn more than expected).

Fields of papers citing papers by Bernardo Cockburn

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Bernardo Cockburn. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Bernardo Cockburn. The network helps show where Bernardo Cockburn may publish in the future.

Co-authorship network of co-authors of Bernardo Cockburn

This figure shows the co-authorship network connecting the top 25 collaborators of Bernardo Cockburn. A scholar is included among the top collaborators of Bernardo Cockburn based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Bernardo Cockburn. Bernardo Cockburn is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

Sort: Min cites: Since: Top N: Style:

20 of 20 papers shown

#	Work	Indexed citations
1	Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems 2023 ·Frontiers in Applied Mathematics and Statistics ·Bernardo Cockburn, (unknown), (unknown)	2
2	A priori error analysis of new semidiscrete, Hamiltonian HDG methods for the time-dependent Maxwell’s equations 2023 ·ESAIM. Mathematical modelling and numerical analysis ·Bernardo Cockburn, (unknown), (unknown)	0
3	Symplectic Hamiltonian finite element methods for electromagnetics 2022 ·Computer Methods in Applied Mechanics and Engineering ·(unknown), (unknown), Bernardo Cockburn, Ngoc Cuong Nguyen, J. Peraire	6
4	An adjoint-based adaptive error approximation of functionals by the hybridizable discontinuous Galerkin method for second-order elliptic equations 2022 ·Journal of Computational Physics ·Bernardo Cockburn, Shiqiang Xia	3
5	Symplectic Hamiltonian finite element methods for linear elastodynamics 2021 ·Computer Methods in Applied Mechanics and Engineering ·(unknown), Bernardo Cockburn, Ngoc Cuong Nguyen, J. Peraire	17
6	An adjoint-based super-convergent Galerkin approximation of eigenvalues 2021 ·Journal of Computational Physics ·Bernardo Cockburn, Shiqiang Xia	1
7	Superconvergent Interpolatory HDG Methods for Reaction Diffusion Equations II: HHO-Inspired Methods 2021 ·Communications on Applied Mathematics and Computation ·Gang Chen, Bernardo Cockburn, John R. Singler, Yangwen Zhang	0
8	Influence of tissue viscoelasticity on the optic nerve head perfusion: a mathematical model 2016 ·Investigative Ophthalmology & Visual Science ·(unknown), Riccardo Sacco, Bernardo Cockburn, Lorena Bociu, Justin T. Webster, Brent Siesky, Alon Harris, Giovanna Guidoboni	1
9	Contraction property of adaptive hybridizable discontinuous Galerkin methods 2015 ·Mathematics of Computation ·Bernardo Cockburn, Ricardo H. Nochetto, Wujun Zhang	8
10	Discontinuous Galerkin Methods: Theory, Computation and Applications breakdown → 2011 ·CERN Document Server (European Organization for Nuclear Research) ·Bernardo Cockburn, George Em Karniadakis, Chi‐Wang Shu	415
11	A new elasticity element made for enforcing weak stress symmetry 2010 ·Mathematics of Computation ·Bernardo Cockburn, Jay Gopalakrishnan, Johnny Guzmán	83
12	Hybridized globally divergence-free LDG methods. Part I: The Stokes problem 2005 ·Mathematics of Computation ·(unknown), Bernardo Cockburn, Dominik Schötzau	74
13	Continuous Dependence on the Nonlinearity of Viscosity Solutions of Parabolic Equations 2001 ·Journal of Differential Equations ·Bernardo Cockburn, Gustaf Gripenberg, Stig–Olof Londen	8
14	Devising discontinuous Galerkin methods for non-linear hyperbolic conservation laws 2001 ·Journal of Computational and Applied Mathematics ·Bernardo Cockburn	66
15	A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach 1996 ·Mathematics of Computation ·Bernardo Cockburn, Pierre-Alain Gremaud	31
16	On Convergence to Entropy Solutions of a Single Conservation Law 1996 ·Journal of Differential Equations ·Bernardo Cockburn, Gustaf Gripenberg, (unknown)	16
17	Determining degrees of freedom for nonlinear dissipative equations 1995 ·University of Minnesota Digital Conservancy (University of Minnesota) ·Bernardo Cockburn, D. A. Jones, Edriss S. Titi	19
18	Error Estimates for a Finite Element Method for the Drift-Diffusion Semiconductor Device Equations: The Zero Diffusion Case 1994 ·Mathematics of Computation ·Bernardo Cockburn, Ioana Triandaf	6
19	An error estimate for finite volume methods for multidimensional conservation laws 1994 ·Mathematics of Computation ·Bernardo Cockburn, Fré́dé́ric Coquel, Philippe G. LeFloch	50
20	Convergence of a Finite Element Method for the Drift-Diffusion Semiconductor Device Equations: The Zero Diffusion Case 1992 ·Mathematics of Computation ·Bernardo Cockburn, Ioana Triandaf	3

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

Explore authors with similar magnitude of impact