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Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems

✍ Scribed by Raytcho Lazarov; Sergey Repin; Satyendra K. Tomar

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
261 KB
Volume
25
Category
Article
ISSN
0749-159X

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✦ Synopsis

Abstract

In this article, we develop functional a posteriori error estimates for discontinuous Galerkin (DG) approximations of elliptic boundary‐value problems. These estimates are based on a certain projection of DG approximations to the respective energy space and functional a posteriori estimates for conforming approximations developed by S. Repin (see e.g., Math Comp 69 (2000) 481–500). On these grounds, we derive two‐sided guaranteed and computable bounds for the errors in “broken” energy norms. A series of numerical examples presented confirm the efficiency of the estimates. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009

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