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.
Mots-clés : Cahn-Hilliard equation, obstacle free energy, linear finite elements, a posteriori estimates, adaptive numerical methods
@article{M2AN_2009__43_5_1003_0, author = {Ba\v{n}as, \v{L}ubom{\'\i}r and N\"urnberg, Robert}, title = {A posteriori estimates for the {Cahn-Hilliard} equation with obstacle free energy}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {1003--1026}, publisher = {EDP-Sciences}, volume = {43}, number = {5}, year = {2009}, doi = {10.1051/m2an/2009015}, mrnumber = {2559742}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2009015/} }
TY - JOUR AU - Baňas, Ľubomír AU - Nürnberg, Robert TI - A posteriori estimates for the Cahn-Hilliard equation with obstacle free energy JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 1003 EP - 1026 VL - 43 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2009015/ DO - 10.1051/m2an/2009015 LA - en ID - M2AN_2009__43_5_1003_0 ER -
%0 Journal Article %A Baňas, Ľubomír %A Nürnberg, Robert %T A posteriori estimates for the Cahn-Hilliard equation with obstacle free energy %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 1003-1026 %V 43 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2009015/ %R 10.1051/m2an/2009015 %G en %F M2AN_2009__43_5_1003_0
Baňas, Ľubomír; Nürnberg, Robert. A posteriori estimates for the Cahn-Hilliard equation with obstacle free energy. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 5, pp. 1003-1026. doi : 10.1051/m2an/2009015. http://archive.numdam.org/articles/10.1051/m2an/2009015/
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