On nonlinear artificial viscosity, discrete maximum principle and hyperbolic conservation laws

Burman, Erik (2007) On nonlinear artificial viscosity, discrete maximum principle and hyperbolic conservation laws. BIT Numerical Mathematics, 47 (4). pp. 715-733. ISSN 0006-3835

Full text not available from this repository.

Abstract

A finite element method for Burgers equation is studied. The method is analyzed using techniques from stabilized finite element methods and convergence to entropy solutions is proven under certain hypotheses on the artificial viscosity. In particular we assume that a discrete maximum principle holds. We then construct a nonlinear artificial viscosity that satisfies the assumptions required for convergence and that can be tuned to minimize artificial viscosity away from local extrema. The theoretical results are exemplified on a numerical example.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 20:57
Last Modified: 10 Jul 2012 12:04
URI: http://sro.sussex.ac.uk/id/eprint/28817
📧 Request an update