NANANov 24, 2014

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

arXiv:1411.6333
Originality Incremental advance
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Provides a novel numerical method for solving reaction-diffusion problems with discontinuous coefficients, which is important for computational science and engineering applications.

The paper introduces a new stabilized discontinuous Galerkin method for reaction-diffusion problems with discontinuous coefficients, proving well-posedness via Inf-Sup condition and deriving a priori error estimates verified by a 2D experiment.

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.

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