Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423280 | Applied Numerical Mathematics | 2011 | 21 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Michael Holst, Jeffrey S. Ovall, Ryan Szypowski,