Some New Local Error Estimates in Negative Norms with an Application to Local a Posteriori Error Estimation
Year: 2006
Author: Alfred H. Schatz
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 3 : pp. 371–376
Abstract
Here we survey some previously published results and announce some that have been newly obtained. We first review some of the results in [3] on estimates for the finite element error at a point. These estimates and analogous ones in [4] and [7] have been applied to problems in a posteriori estimates [2], [8], superconvergence [5] and others [9], [10]. We then discuss the extension of these estimates to local estimates in $L_∞$ based negative norms. These estimates have been newly obtained and are applied to the problem of obtaining an asymptotically exact a posteriori estimator for the maximum norm of the solution error on each element.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-IJNAM-908
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 3 : pp. 371–376
Published online: 2006-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 6
Keywords: superconvergence error estimate a posteriori.