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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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Published in: | SIAM journal on numerical analysis 2002, Vol.39 (4), p.1343-1365 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0036-1429 1095-7170 |
DOI: | 10.1137/S0036142900378480 |