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Superconvergence of discontinuous Galerkin methods for hyperbolic systems

✍ Scribed by Tie Zhang; Jiandong Li; Shuhua Zhang

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
660 KB
Volume
223
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper, the discontinuous Galerkin method for the positive and symmetric, linear hyperbolic systems is constructed and analyzed by using bilinear finite elements on a rectangular domain, and an O(h 2 )-order superconvergence error estimate is established under the conditions of almost uniform partition and the H 3 -regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Finally, as an application, the numerical treatment of Maxwell equation is discussed and computational results are presented.

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