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

@article{Lee2019AHD, title={A hybridized discontinuous Galerkin method for Poisson-type problems with sign-changing coefficients}, author={Jeonghun J. Lee and Sander Rhebergen}, journal={ArXiv}, year={2019}, volume={abs/1911.01984} }

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…

## 2 Citations

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

- Mathematics, Computer ScienceESAIM: Mathematical Modelling and Numerical Analysis
- 2021

This work presents and analyzes a generalized finite element method in the spirit of the localized orthogonal decomposition, that is especially efficient when the negative and positive materials exhibit multiscale features.

### Analysis of hybridized discontinuous Galerkin methods without elliptic regularity assumptions

- Computer Science, MathematicsArXiv
- 2019

New stability and optimal error analyses of hybridized discontinuous Galerkin (HDG) methods which do not require elliptic regularity assumptions are presented and new inf-sup conditions based on stabilized saddle point structures of HDG methods are used.

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