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arXiv · 1911.01984

A hybridized discontinuous Galerkin method for Poisson-type problems with sign-changing coefficients

Jeonghun J. Lee·Sander Rhebergen
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Abstract

In this paper, we present a hybridized discontinuous Galerkin (HDG) method for Poisson-type problems with sign-changing coefficients. We introduce a sign-changing stabilization parameter that results in a stable HDG method independent of domain geometry and the ratio of the negative and positive coefficients. Since the Poisson-type problem with sign-changing coefficients is not elliptic, standard techniques with a duality argument to analyze the HDG method cannot be applied. Hence, we present a novel error analysis exploiting the stabilized saddle-point problem structure of the HDG method. Numerical experiments in two dimensions and for varying polynomial degree verify our theoretical results.

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Jeonghun J. Lee, Sander Rhebergen. 2019-11-11. A hybridized discontinuous Galerkin method for Poisson-type problems with sign-changing coefficients. https://arxiv.org/abs/1911.01984

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