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

by   Jeonghun J. Lee, et al.

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.


page 1

page 2

page 3

page 4


Superconvergence of Discontinuous Galerkin methods for Elliptic Boundary Value Problems

In this paper, we present a unified analysis of the superconvergence pro...

A generalized finite element method for problems with sign-changing coefficients

Problems with sign-changing coefficients occur, for instance, in the stu...

Sign-consistent estimation in a sparse Poisson model

In this work, we consider an estimation method in sparse Poisson models ...

An optimal control-based numerical method for scalar transmission problems with sign-changing coefficients

In this work, we present a new numerical method for solving the scalar t...

About some generalizations trigonometric splines

Methods of constructing trigonometric fundamental splines with constant ...

Computer-assisted analysis of the sign-change structure for elliptic problems

In this paper, a method is proposed for rigorously analyzing the sign-ch...

Please sign up or login with your details

Forgot password? Click here to reset