WorldCat Identities

Cockburn, B. (Bernardo)

Overview
Works: 74 works in 163 publications in 3 languages and 1,603 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Contributor, Editor, htt, Collector, Other
Classifications: QA3, 620.00151535
Publication Timeline
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Most widely held works by B Cockburn
Advanced numerical approximation of nonlinear hyperbolic equations : lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 23-28, 1997 by B Cockburn( Book )

30 editions published between 1998 and 2006 in English and held by 581 WorldCat member libraries worldwide

This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis
Discontinuous Galerkin methods : theory, computation, and applications by B Cockburn( Book )

13 editions published between 2000 and 2009 in English and German and held by 283 WorldCat member libraries worldwide

This volume contains current progress of a new class of finite element method, the Discontinuous Galerkin Method (DGM), which has been under rapid developments recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simulation, turbomachinery, turbulent flows, materials processing, Magneto-hydro-dynamics, plasma simulations and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effect in organizing and publishing the existing volume of knowledge on this subject. The current volume organizes this knowledge and it covers both theoretical as well as practical issues of the Discontinuous Galerkin method
The P¹-RKDG method for two-dimensional Euler equations of gas dynamics by B Cockburn( Book )

2 editions published in 1991 in English and held by 134 WorldCat member libraries worldwide

Earlier work is continued on a class on nonlinearly stable Runge Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws. Two dimensional Euler equations for gas dynamics are solved using p1 elements. We discuss the generalization of the local projection, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions. Numerical examples include the standard regular shock reflection problem, the forward facing step problem and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of our approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods. Generalizations to pk elements with k equal to or greater than the use of adaptive triangulations to minimize local errors constitute ongoing research
Runge-Kutta discontinuous Galerkin methods for convection-dominated problems by B Cockburn( Book )

4 editions published in 2000 in English and held by 105 WorldCat member libraries worldwide

Enhanced accuracy by post-processing for finite element methods for hyperbolic equations by B Cockburn( Book )

4 editions published in 2000 in English and held by 103 WorldCat member libraries worldwide

Nonlinearly stable compact schemes for shock calculations by B Cockburn( Book )

5 editions published in 1992 in English and held by 94 WorldCat member libraries worldwide

In this paper we discuss the applications of high order compact finite difference methods for shock calculations. The main idea is the definition of a local mean which serves as a reference for introducing a local nonlinear limiting to control spurious numerical oscillations while keeping the formal accuracy of the scheme. For scalar conservation laws, the resulting schemes can be proven total variation stable in one space dimension and maximum norm stable in multiple space dimensions. Numerical examples are shown to verify accuracy and stability of such schemes for problems containing shocks. The idea in this paper can also be applied to other implicit schemes such as the continuous Galerkin finite element methods
The Local Discontinuous Galerkin method for time-dependent convection-diffusion systems by B Cockburn( Book )

6 editions published in 1997 in English and held by 93 WorldCat member libraries worldwide

In this paper, we study the Local Discontinuous Galerkin methods for non-linear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L2-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown
The Runge-Kutta discontinuous Galerkin method for conservation laws V : multidimensional systems by B Cockburn( Book )

5 editions published in 1997 in English and held by 90 WorldCat member libraries worldwide

This is the fifth paper in a series in which we construct and study the so-called Range-Kutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are described and discussed, including algorithm formulation and practical implementation issues such as the numerical fluxes, quadrature rules, degrees of freedom, and the slope limiters, both in the triangular and the rectangular element cases. Numerical experiments for two dimensional Euler equations of compressible gas dynamics are presented that show the effect of the (formal) order of accuracy and the use of triangles or rectangles, on the quality of the approximation
Étude mathématique et numérique des équations de Maxwell dans des milieux polarisables by B Cockburn( )

5 editions published between 1983 and 2019 in French and held by 10 WorldCat member libraries worldwide

Formulation du problème par l'équation intégrale de Volterra. Approximation du noyau de convolation par un opérateur différentiel. Analyse numérique; stabilité et convergence du schéma numérique
Discontinuous Galerkin Methods : Theory, Computation and Applications( )

in English and held by 7 WorldCat member libraries worldwide

The local discontinuous Galerkin method for linear incompressible fluid flow a review by B Cockburn( Book )

2 editions published in 2003 in English and held by 7 WorldCat member libraries worldwide

A locally conservative LDG method for the incompressible Navier Stokes equations by B Cockburn( Book )

2 editions published in 2004 in English and held by 7 WorldCat member libraries worldwide

Consistance et stabilite des schemas LRG pour les lois de conservation scalaires by Guy Chavent( Book )

3 editions published in 1987 in French and held by 6 WorldCat member libraries worldwide

Le schéma G-k/2 pour les lois de conservation scalaires by B Cockburn( Book )

4 editions published in 1985 in French and held by 4 WorldCat member libraries worldwide

A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations by B Cockburn( )

1 edition published in 2006 in English and held by 3 WorldCat member libraries worldwide

On convergence to entropy solutions of a single conservation law by B Cockburn( Book )

3 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide

Stormer-Numerov HDG Methods for Acoustic Waves by B Cockburn( )

1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide

The Pl-RKDG method for two-dimensional Euler equations of gas dynamics by B Cockburn( Book )

1 edition published in 1991 in English and held by 2 WorldCat member libraries worldwide

Nonlinearly stable compact schemes for shock calculations by B Cockburn( Book )

2 editions published in 1992 in English and held by 2 WorldCat member libraries worldwide

Une Méthode d'éléments finis pour la simulation dans un réservoir de déplacements bidimensionnels d'huile par de l'eau by Institut national de recherche en informatique et en automatique (France)( Book )

2 editions published in 1985 in French and held by 2 WorldCat member libraries worldwide

 
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Advanced numerical approximation of nonlinear hyperbolic equations : lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 23-28, 1997
Covers
Discontinuous Galerkin methods : theory, computation, and applications
Alternative Names
Cockburn, B.

Cockburn, B. 19XX-

Cockburn,(Bernardo

Cockburn, Bernardo 1956-

Languages
English (81)

French (14)

German (1)