A posteriori error estimates in the maximum norm for parabolic problems

Details A posteriori error estimates in the maximum norm for parabolic problems A posteriori error estimates in the maximum norm for parabolic problems

2007-11-25

arxiv.org/abs/0711.3928v1

SIAM Journal on Numerical Analysis 2009 vol. 47 (3) pp. 2157-2176

Mathematics

Numerical Analysis

Scientific paper

10.1137/070708792

We derive a posteriori error estimates in the $L_\infty((0,T];L_\infty(\Omega))$ norm for approximations of solutions to linear para bolic equations. Using the elliptic reconstruction technique introduced by Makridakis and Nochetto and heat kernel estimates for linear parabolic pr oblems, 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 allow\ ing the straightforward combination of heat kernel estimates with existing elliptic maximum norm error estimators.

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