A multigrid method for the Cahn-Hilliard equation with obstacle potential |
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Authors: | L’ubomír Baňas Robert Nürnberg |
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Institution: | a Department of Mathematics and The Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK b Department of Mathematics, Imperial College London, London SW7 2AZ, UK |
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Abstract: | We present a multigrid finite element method for the deep quench obstacle Cahn-Hilliard equation. The non-smooth nature of this highly nonlinear fourth order partial differential equation make this problem particularly challenging. The method exhibits mesh-independent convergence properties in practice for arbitrary time step sizes. In addition, numerical evidence shows that this behaviour extends to small values of the interfacial parameter γ. Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn-Hilliard equation. |
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Keywords: | Cahn-Hilliard equation Obstacle free energy Finite elements Multigrid method |
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