Analysis of a new stabilized discontinuous Galerkin method for the reaction-diffusion problem with discontinuous coefficient

TL;DR

This paper introduces a novel stabilized discontinuous Galerkin method with an added stabilization term, ensuring local conservation and well-posedness, and provides error estimates validated through 2D experiments on reaction-diffusion problems.

Contribution

The paper presents a new stabilized DG method with a unique function space and stabilization term, differing from existing methods, and proves its theoretical properties with numerical validation.

Findings

Method satisfies local conservation property.

Proven well-posedness via Inf-Sup condition.

Error estimates confirmed by 2D experiments.

Abstract

In this paper, a new stabilized discontinuous Galerkin method within a new function space setting is introduced, which involves an extra stabilization term on the normal fluxes across the element interfaces. It is different from the general DG methods. The formulation satisfies a local conservation property and we prove well posedness of the new formulation by Inf-Sup condition. A priori error estimates are derived, which are verified by a 2D experiment on a reaction-diffusion type model problem.