Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes

Burman, Erik and Ern, Alexandre (2004) Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes. Comptes Rendus Mathématique, 338 (8). pp. 641-646. ISSN 1631-073X

Full text not available from this repository.

Abstract

We derive a nonlinear stabilized Galerkin approximation of the Laplace operator for which we prove a discrete maximum principle on arbitrary meshes and for arbitrary space dimension without resorting to the well-known acute condition or generalizations thereof. We also prove the existence of a discrete solution and discuss the extension of the scheme to convectiondiffusionreaction equations. Finally, we present examples showing that the new scheme cures local minima produced by the standard Galerkin approach while maintaining first-order accuracy in the H1-norm.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 18:26
Last Modified: 13 Jun 2012 11:12
URI: http://sro.sussex.ac.uk/id/eprint/16323
📧 Request an update