Issue ESAIM: M2AN Volume 43, Number 5, September-October 2009 Page(s) 1003 - 1026 DOI 10.1051/m2an/2009015 Published online 12 June 2009

ESAIM: M2AN 43 (2009) 1003-1026
DOI: 10.1051/m2an/2009015

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

Ľubomír Baňas¹ and Robert Nürnberg<sup>2

1</sup>  Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK. L.Banas@hw.ac.uk
²  Department of Mathematics, Imperial College London, London, SW7 2AZ, UK.

Received January 14, 2008. Revised November 28, 2008. Published online June 12, 2009.

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.

Mathematics Subject Classification. 65M60, 65M15, 65M50, 35K55

Key words: Cahn–Hilliard equation, obstacle free energy, linear finite elements, a posteriori estimates, adaptive numerical methods


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