Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems

Authors:	Omar Lakkis Charalambos Makridakis

Institution:	Department of Mathematics, University of Sussex, Brighton, UK-BN1 9RF, United Kingdom ; Department of Applied Mathematics, University of Crete, GR-71409 Heraklion, Greece; and Institute for Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Vasilika Vouton P.O. Box 1527, GR-71110 Heraklion, Greece

Abstract:	We derive a posteriori error estimates for fully discrete approximations to solutions of linear parabolic equations. The space discretization uses finite element spaces that are allowed to change in time. Our main tool is an appropriate adaptation of the elliptic reconstruction technique, introduced by Makridakis and Nochetto. We derive novel a posteriori estimates for the norms of $\operatorname{L}_\infty(0,T;\operatorname{L}_2(\Omega))$ and the higher order spaces, $\operatorname{L}_\infty(0,T;\operatorname{H}^1(\Omega))$ and $\operatorname{H}^1(0,T;\operatorname{L}_2(\Omega))$ , with optimal orders of convergence.

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