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

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

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 th...

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Veröffentlicht in:ESAIM. Mathematical modelling and numerical analysis 2009-09, Vol.43 (5), p.1003-1026
Hauptverfasser: Banas, Lubomír, Nürnberg, Robert
Format: Artikel
Sprache:eng
Schlagworte:
35K55
65M15
65M50
65M60
a posteriori estimates
Adaptation
adaptive numerical methods
Approximation
Cahn–Hilliard equation
Control theory
Energy
Estimates
Exact sciences and technology
Heuristic
linear finite elements
Mathematical analysis
Mathematics
Numerical analysis
obstacle free energy
Phase transitions
Sciences and techniques of general use
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Beschreibung
Zusammenfassung: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.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2009015