H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 74 Citations 37,831 182 World Ranking 90 National Ranking 54

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Geometry
  • Partial differential equation

His main research concerns Discontinuous Galerkin method, Mathematical analysis, Galerkin method, Finite element method and Runge–Kutta methods. Bernardo Cockburn interconnects Superconvergence, Applied mathematics, Discretization, Rate of convergence and Conservation law in the investigation of issues within Discontinuous Galerkin method. The study incorporates disciplines such as Projection and Stokes flow in addition to Mathematical analysis.

His research integrates issues of Elliptic curve, Compressibility, Divergence and Order of accuracy in his study of Galerkin method. His work carried out in the field of Finite element method brings together such families of science as Boundary value problem, Norm, Hyperbolic partial differential equation, Computation and Calculus. In his study, which falls under the umbrella issue of Runge–Kutta methods, Exact solutions in general relativity and Shallow water equations is strongly linked to Euler equations.

His most cited work include:

  • Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems (2572 citations)
  • The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems (1790 citations)
  • TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework (1691 citations)

What are the main themes of his work throughout his whole career to date?

His primary scientific interests are in Discontinuous Galerkin method, Mathematical analysis, Finite element method, Applied mathematics and Superconvergence. His study in Discontinuous Galerkin method is interdisciplinary in nature, drawing from both Galerkin method, Degree, Runge–Kutta methods, Rate of convergence and Stokes flow. His Galerkin method research is multidisciplinary, relying on both Discontinuity and Stiffness matrix.

His research on Mathematical analysis frequently connects to adjacent areas such as Projection. His work deals with themes such as Upwind scheme, Lagrange multiplier, Geometry and Hyperbolic partial differential equation, which intersect with Finite element method. His research investigates the connection between Applied mathematics and topics such as Polygon mesh that intersect with issues in Linear elasticity.

He most often published in these fields:

  • Discontinuous Galerkin method (75.96%)
  • Mathematical analysis (63.94%)
  • Finite element method (37.02%)

What were the highlights of his more recent work (between 2012-2021)?

  • Discontinuous Galerkin method (75.96%)
  • Superconvergence (27.88%)
  • Mathematical analysis (63.94%)

In recent papers he was focusing on the following fields of study:

His primary areas of investigation include Discontinuous Galerkin method, Superconvergence, Mathematical analysis, Applied mathematics and Finite element method. His studies in Discontinuous Galerkin method integrate themes in fields like Polygon mesh, Order, Galerkin method, Exact solutions in general relativity and Scalar. His Galerkin method study combines topics in areas such as Norm and Stiffness matrix.

His Mathematical analysis research is multidisciplinary, incorporating elements of Acoustic wave equation, Navier–Stokes equations, Compressibility and Stokes flow. Bernardo Cockburn combines subjects such as Simplex, Rate of convergence, Simple and Mathematical optimization with his study of Applied mathematics. His research in Finite element method intersects with topics in Tetrahedron and Helmholtz equation.

Between 2012 and 2021, his most popular works were:

  • Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods (114 citations)
  • A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations (67 citations)
  • Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations (58 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Geometry
  • Algebra

Bernardo Cockburn focuses on Discontinuous Galerkin method, Mathematical analysis, Superconvergence, Applied mathematics and Finite element method. The concepts of his Discontinuous Galerkin method study are interwoven with issues in Displacement, Exact solutions in general relativity, Galerkin method and Polygon mesh. Bernardo Cockburn has included themes like Multigrid algorithm, Multigrid method, Norm and Prolongation in his Galerkin method study.

His Mathematical analysis research is multidisciplinary, incorporating perspectives in Rate of convergence, Compressibility, Order and Degree. His study looks at the intersection of Superconvergence and topics like Acoustic wave equation with Scalar field, Wave equation, Runge–Kutta methods and Upwind scheme. His studies deal with areas such as Simple and Mathematical optimization as well as Applied mathematics.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Top Publications

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

Douglas N. Arnold;Franco Brezzi;Bernardo Cockburn;L. Donatella Marini.
SIAM Journal on Numerical Analysis (2001)

3533 Citations

The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V

Bernardo Cockburn;Chi-Wang Shu.
Journal of Computational Physics (1998)

2356 Citations

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

Bernardo Cockburn;Chi Wang Shu.
Mathematics of Computation (1989)

2341 Citations

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

Bernardo Cockburn;Chi-Wang Shu;Chi-Wang Shu.
SIAM Journal on Numerical Analysis (1998)

2274 Citations

The Development of Discontinuous Galerkin Methods

Bernardo Cockburn;George E. Karniadakis;Chi-Wang Shu.
(2000)

2053 Citations

Runge-Kutta discontinuous Galerkin methods for convection-dominated problems

Bernardo Cockburn;Chi-Wang Shu.
(2000)

1862 Citations

Regular ArticleThe Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V: Multidimensional Systems☆

Bernardo Cockburn;Chi-Wang Shu.
Journal of Computational Physics (1998)

1739 Citations

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.
Mathematics of Computation (1990)

1647 Citations

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.
Journal of Computational Physics (1989)

1473 Citations

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

Bernardo Cockburn;Jayadeep Gopalakrishnan;Raytcho Lazarov.
SIAM Journal on Numerical Analysis (2009)

967 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

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