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

2019/11/05 by Jeonghun J. Lee, Lee, Jeonghun J., Sander Rhebergen +1
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)

paper · pdf · doi:10.48550/arxiv.1911.01984

openalex publication_date 2019/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates

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