Bernardo Cockburn
- Publications
- Influence
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We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous… Continue Reading
In this paper, we study the local discontinuous Galerkin (LDG) methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge--Kutta discontinuous… Continue Reading
In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way… Continue Reading
Construction et analyse d'une classe de methodes a elements finis de Galerkin discontinues a variation totale bornee pour la resolution des lois de conservation. Etude de la convergence. Resultats… Continue Reading
This is the fifth paper in a series in which we construct and study the so-called Runge?Kutta discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we… Continue Reading
We introduce a unifying framework for hybridization of finite element methods for second order elliptic problems. The methods fitting in the framework are a general class of mixed-dual finite element… Continue Reading
In this paper we study the two-dimensional version of the Runge- Kutta Local Projection Discontinuous Galerkin (RKDG) methods, already de- fined and analyzed in the one-dimensional case. These… Continue Reading
This is the third paper in a series in which we construct and analyze a class of TVB (total variation bounded) discontinuous Galerkin finite element methods for solving conservation laws… Continue Reading
We consider the enhancement of accuracy, by means of a simple post-processing technique, for finite element approximations to transient hyperbolic equations. The post-processing is a convolution with… Continue Reading
In this paper, we present the first a priori error analysis for the local discontinuous Galerkin (LDG) method for a model elliptic problem. For arbitrary meshes with hanging nodes and elements of… Continue Reading