An efficient, reliable and robust error estimator for elliptic problems in R3

• Autores: Michael Holst, Jeffrey S. Ovall, Ryan Szypowski
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 61, Nº. 5, 2011, págs. 675-695
• Idioma: inglés
• DOI: 10.1016/j.apnum.2011.01.002
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• Resumen

  • In this article, we develop and analyze a hierarchical-type error estimator for a general class of second-order linear elliptic boundary value problems in bounded three-dimensional domains. This type of indicator automatically satisfies a global lower bound inequality, thereby giving efficiency, without regularity assumptions beyond those giving well-posedness of the continuous and discrete problems. The main focus of the paper is then to establish the reverse reliability result: a global upper bound on the error in terms of the error estimate (plus an oscillation term), again without additional regularity assumptions. The proof of this inequality depends on a clever choice of the space in which the error indicator lies and a moment-capturing quasi-interpolation result. We finish the article with a series of numerical experiments to illustrate the behavior predicted by the theoretical results.