A hybridized discontinuous Galerkin method for Poisson-type problems with sign-changing coefficients
Numerical Analysis
2019-11-12 v2 Numerical Analysis
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.
Cite
@article{arxiv.1911.01984,
title = {A hybridized discontinuous Galerkin method for Poisson-type problems with sign-changing coefficients},
author = {Jeonghun J. Lee and Sander Rhebergen},
journal= {arXiv preprint arXiv:1911.01984},
year = {2019}
}