Discontinuous Galerkin Methods for Second-Order Elliptic Problems with Discontinuous Coefficients

Daniele Di Pietro, Alexandre Ern, Jean-Luc Guermond

Abstract


In this work we analyze a class of discontinuous Galerkin methods (DG) for second-order elliptic problems with discontinuous coefficients. The lower regularity of the coefficients requires some modifications of the Friedrichs formalism introduced by Ern and Guermond (2005). After rewriting the problem in mixed form, we prove the well-posedness of the continuous problem and examine two possible strategies for the design of a DG approximation. In both cases we present a complete analysis of the resulting methods based on Strang's second lemma. All the design constraints on boundary and interface operators are fully stated and the link with the flux formulation is discussed.

[DOI: 10.1685/CSC06068] About DOI

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DOI: http://dx.doi.org/10.1685/




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