Minimal Stabilization for Discontinuous Galerkin Finite Element Methods for Hyperbolic Problems

Authors:
E. Burman;B. Stamm
Affiliations:
Institute of Analysis and Scientific Computing, Swiss Institute of Technology, Lausanne, Switzerland;Institute of Analysis and Scientific Computing, Swiss Institute of Technology, Lausanne, Switzerland
Venue:
Journal of Scientific Computing
Year:
2007

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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 graphnorm and obtain optimal order error estimates with respect to mesh-size.