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Adaptive finite element methods for Cahn–Hilliard equations

✍ Scribed by L’ubomír Baňas; Robert Nürnberg

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
883 KB
Volume
218
Category
Article
ISSN
0377-0427

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✦ Synopsis

We develop a method for adaptive mesh refinement for steady state problems that arise in the numerical solution of Cahn-Hilliard equations with an obstacle free energy. The problem is discretized in time by the backward-Euler method and in space by linear finite elements. The adaptive mesh refinement is performed using residual based a posteriori estimates; the time step is adapted using a heuristic criterion. We describe the space-time adaptive algorithm and present numerical experiments in two and three space dimensions that demonstrate the usefulness of our approach.

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