Commun. Comput. Phys., 11 (2012), pp. 1043-1080.


A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art

Remi Abgrall 1*

1 Team Bacchus, Institut de Mathematiques de Bordeaux, INRIA and University of Bordeaux, 33 405 Talence cedex, France.

Received 27 July 2010; Accepted (in revised version) 13 July 2011
Available online 29 November 2011
doi:10.4208/cicp.270710.130711s

Abstract

We describe and review non oscillatory residual distribution schemes that are rather natural extension of high order finite volume schemes when a special emphasis is put on the structure of the computational stencil. We provide their connections with standard stabilized finite element and discontinuous Galerkin schemes, show that their are really non oscillatory. We also discuss the extension to these methods to parabolic problems. We also draw some research perspectives.

AMS subject classifications: 65M60, 76M30, 76M12

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Key words: Hyperbolic problems, Navier Stokes equations, unstructured meshes, residual distribution methods.

*Corresponding author.
Email: remi.abgrall@inria.fr (R. Abgrall)
 

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