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A posteriori error estimates for a nonconforming finite elementdiscretization of the heat equation

Published online by Cambridge University Press:  15 April 2005

Serge Nicaise  and
Nadir Soualem
Serge Nicaise
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, MACS, ISTV, 59313 Valenciennes Cedex 9, France. Serge.Nicaise@univ-valenciennes.fr; Nadir.Soualem@univ-valenciennes.fr
Nadir Soualem
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, MACS, ISTV, 59313 Valenciennes Cedex 9, France. Serge.Nicaise@univ-valenciennes.fr; Nadir.Soualem@univ-valenciennes.fr
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Abstract

The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equationin $\mathbb{R}^d$ , d=2 or 3,using backward Euler's scheme. For this discretization, we derive a residual indicator, which usea spatial residual indicator based on thejumps of normal and tangential derivatives of the nonconformingapproximation and a time residual indicator based on the jump of broken gradients at each time step.Lower and upper bounds form the main results with minimal assumptions on the mesh.Numerical experiments and a space-time adaptive algorithm confirm the theoretical predictions.

Keywords

Error estimatornonconforming FEMheat equation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 2 , March 2005 , pp. 319 - 348
Copyright
© EDP Sciences, SMAI, 2005

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