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

Lakkis, Omar; Makridakis, Charalambos

doi:10.1090/S0025-5718-06-01858-8

Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
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by Omar Lakkis and Charalambos Makridakis PDF

Math. Comp. 75 (2006), 1627-1658 Request permission

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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