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Two-Level Additive Schwarz Methods for a Discontinuous Galerkin Approximation of Second Order Elliptic Problems

We present some two-level nonoverlapping and overlapping additive Schwarz methods for a discontinuous Galerkin method for solving second order elliptic problems. It is shown that the condition numbers of the preconditioned systems are of the order $O({H \over {h}})$ for the nonoverlapping Schwarz me...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2002, Vol.39 (4), p.1343-1365
Main Authors: Feng, Xiaobing, Karakashian, Ohannes A.
Format: Article
Language:English
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Summary:We present some two-level nonoverlapping and overlapping additive Schwarz methods for a discontinuous Galerkin method for solving second order elliptic problems. It is shown that the condition numbers of the preconditioned systems are of the order $O({H \over {h}})$ for the nonoverlapping Schwarz methods and of the order $O({H \over {\delta}})$ for the overlapping Schwarz methods, where h and H stand for the fine-mesh size and the coarse-mesh size, respectively, and δ denotes the size of the overlaps between subdomains. Numerical experiments are provided to gauge the efficiency of the methods and to validate the theory.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142900378480