Geodesic
A posteriori estimates for the Cahn-Hilliard equation with obstacle free energy
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 5, pp. 1003-1026

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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.

DOI : 10.1051/m2an/2009015
Classification : 65M60, 65M15, 65M50, 35K55
Keywords: Cahn-Hilliard equation, obstacle free energy, linear finite elements, a posteriori estimates, adaptive numerical methods 
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     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: Mathematical Modelling and Numerical Analysis },
     pages = {1003--1026},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {5},
     year = {2009},
     doi = {10.1051/m2an/2009015},
     mrnumber = {2559742},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2009015/}
}
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Baňas, Ľubomír; Nürnberg, Robert. A posteriori estimates for the Cahn-Hilliard equation with obstacle free energy. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 5, pp. 1003-1026. doi: 10.1051/m2an/2009015

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