Additive Schwarz Methods for DG Discretization of Elliptic Problems with Discontinuous Coefficient
Second order elliptic problem with discontinuous coefficient in 2-D is considered. The problem is discretized by a symmetric interior penalty discontinuous Galerkin (DG) finite element method with triangular elements and piecewise linear functions. The resulting discrete problem is solved by a two-level additive Schwarz method. It turns out that the rate of convergence of the method is independent of the jumps of coefficient if its variation inside substructures is bounded. Numerical experiments are reported which confirm theoretical results.
KeywordsAdditive Schwarz method Discontinuous Galerkin Nonconforming
We would like to thank an anonymous referee whose comments and remarks helped to improve the paper. This research has been supported by the Polish National Science Centre grant 2011/01/B/ST1/01179.
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