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.
@article{M2AN_2009__43_5_1003_0,
author = {Ba\v nas, \v Lubom\'\i r and N\"urnberg, Robert},
title = {A posteriori estimates for the Cahn-Hilliard equation with obstacle free energy},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {43},
year = {2009},
pages = {1003-1026},
doi = {10.1051/m2an/2009015},
mrnumber = {2559742},
zbl = {pre05608360},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2009__43_5_1003_0}
}
Baňas, Ľubomír; Nürnberg, Robert. A posteriori estimates for the Cahn-Hilliard equation with obstacle free energy. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) pp. 1003-1026. doi : 10.1051/m2an/2009015. http://gdmltest.u-ga.fr/item/M2AN_2009__43_5_1003_0/
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