# A Posteriori Error Estimates in the Maximum Norm for Parabolic Problems

Demlow, Alan, Lakkis, Omar and Makridakis, Charalambos (2009) A Posteriori Error Estimates in the Maximum Norm for Parabolic Problems. SIAM Journal on Numerical Analysis, 47 (3). pp. 2157-2176. ISSN 0036-1429

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## Abstract

We derive a posteriori error estimates in the $L_\infty((0,T];L_\infty(\Omega))$ norm for approximations of solutions to linear parabolic equations. Using the elliptic reconstruction technique introduced by Makridakis and Nochetto and heat kernel estimates for linear parabolic problems, we first prove a posteriori bounds in the maximum norm for semidiscrete finite element approximations. We then establish a posteriori bounds for a fully discrete backward Euler finite element approximation. The elliptic reconstruction technique greatly simplifies our development by allowing the straightforward combination of heat kernel estimates with existing elliptic maximum norm error estimators.

Item Type: Article School of Mathematical and Physical Sciences > Mathematics Omar Lakkis 06 Feb 2012 19:26 04 Apr 2012 08:55 http://srodev.sussex.ac.uk/id/eprint/20583