2019/11/05 by Jeonghun J. Lee, Lee, Jeonghun J., Sander Rhebergen +1 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1911.01984
openalex publication_date 2019/11/05 · arxiv created 2019/11/11 · arxiv updated 2019/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.