A Posteriori Error Estimates for Parabolic Variational Inequalities

Authors:
Yves Achdou;Frédéric Hecht;David Pommier
Affiliations:
UFR Mathématiques, Université Paris Diderot, Paris Cedex 05, France 75251 and Laboratoire Jacques-Louis Lions, Université Paris 6, Paris Cedex 05, France 75252;Laboratoire Jacques-Louis Lions, Université Paris 6, Paris Cedex 05, France 75252;Projet MATHFI---INRIA Rocquencourt, Le Chesnay Cedex, France 78153
Venue:
Journal of Scientific Computing
Year:
2008

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Abstract

We study a posteriori error estimates in the energy norm for some parabolic obstacle problems discretized with a Euler implicit time scheme combined with a finite element spatial approximation. We discuss the reliability and efficiency of the error indicators, as well as their localization properties. Apart from the obstacle resolution, the error indicators vanish in the so-called full contact set. The case when the obstacle is piecewise affine is studied before the general case. Numerical examples are given.