Commun. Comput. Phys., 5 (2009), pp. 376-390.


Development of Residual Distribution Schemes for the Discontinuous Galerkin Method: The Scalar Case with Linear Elements

Remi Abgrall 1*, Chi-Wang Shu 2

1 Institut de Mathematiques and INRIA, Universite Bordeaux I, 341 cours de la Liberation, 33 405 Talence cedex, France.
2 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.

Received 30 September 2007; Accepted (in revised version) 31 March 2008
Available online 1 August 2008

Abstract

In this paper, we reformulate the piecewise linear discontinuous Galerkin (DG) method for solving two dimensional steady state scalar conservation laws in the framework of residual distribution (RD) schemes. This allows us to propose a new class of nonlinear stabilization that does not destroy the formal accuracy of the schemes. Numerical results are shown to demonstrate the behavior of this approach.

AMS subject classifications: 65N30, 65N99, 65M60, 65M99

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Key words: Discontinuous Galerkin schemes, residual distribution schemes, high order, unstructured meshes.

*Corresponding author.
Email: abgrall@math.u-bordeaux.fr (R. Abgrall), shu@dam.brown.edu (C.-W. Shu)
 

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