A posteriori estimates for the Cahn–Hilliard equation with obstacle free energy
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.
Revised: 28 November 2008
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
© EDP Sciences, SMAI, 2009