Commun. Comput. Phys., 5 (2009), pp. 498-514.


Local Discontinuous Galerkin Method with Reduced Stabilization for Diffusion Equations

E. Burman 1, B. Stamm 2*

1 Department of Mathematics, Mantell Building, University of Sussex, Falmer, Brighton, BN1 9RF, UK.
2 Institute of Analysis and Scientific Computing, Swiss Institute of Technology, Lausanne, CH-1015, Switzerland.

Received 2 October 2007; Accepted (in revised version) 8 May 2008
Available online 1 August 2008

Abstract

We extend the results on minimal stabilization of Burman and Stamm [J. Sci. Comp., 33 (2007), pp.~183-208] to the case of the local discontinuous Galerkin methods on mixed form. The penalization term on the faces is relaxed to act only on a part of the polynomial spectrum. Stability in the form of a discrete inf-sup condition is proved and optimal convergence follows. Some numerical examples using high order approximation spaces illustrate the theory.

AMS subject classifications: 65N30, 35F15

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Key words: Local discontinuous Galerkin h-FEM, interior penalty, diffusion equation.

*Corresponding author.
Email: E.N.Burman@sussex.ac.uk (E. Burman), benjamin.stamm@epfl.ch (B. Stamm)
 

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