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A posteriori estimates for the Cahn–Hilliard equation with obstacle free energy

Published online by Cambridge University Press:  12 June 2009

Ľubomír Baňas  and
Robert Nürnberg
Ľubomír Baňas
Affiliation:
Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK. L.Banas@hw.ac.uk
Robert Nürnberg
Affiliation:
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK.
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Abstract

We derive a posteriori estimates for a discretization in space of the standard Cahn–Hilliard equation with a double obstacle free energy. The derived estimates are robust and efficient, and in practice are combined with a heuristic time step adaptation. We present numerical experiments in two and three space dimensions and compare our method with an existing heuristic spatial mesh adaptation algorithm.

Keywords

Cahn–Hilliard equationobstacle free energylinear finite elementsa posteriori estimatesadaptive numerical methods
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 5 , September 2009 , pp. 1003 - 1026
Copyright
© EDP Sciences, SMAI, 2009

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