Minimal stabilization for discontinuous Galerkin finite element methods for hyperbolic problems.

Burman, E and Stamm, B (2007) Minimal stabilization for discontinuous Galerkin finite element methods for hyperbolic problems. Journal of Scientific Computing, 33 (2). 183 - 208. ISSN 0885-7474

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Abstract

We consider a discontinuous Galerkin finite element method for the advection-reaction equation in two space-dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained by a penalization of only the upper portion of the polynomial spectrum of the jump of the solution over element edges. We prove stability in the standard $h$-weighted graph norm and obtain optimal order error estimates with respect to mesh-size.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 21:27
Last Modified: 11 Apr 2012 10:51
URI: http://sro.sussex.ac.uk/id/eprint/31286
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