A multigrid method for the Cahn-Hilliard equation with obstacle potential

Lubomir Banas; Robert Nürnberg

doi:10.1016/j.amc.2009.03.036

A multigrid method for the Cahn-Hilliard equation with obstacle potential

Lubomir Banas, Robert Nürnberg

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

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 ?. Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn-Hilliard equation. © 2009 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	290-303
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	213
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2009.03.036
Publication status	Published - 15 Jul 2009

Keywords

Cahn-Hilliard equation
Finite elements
Multigrid method
Obstacle free energy

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10.1016/j.amc.2009.03.036

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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 ?. Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn-Hilliard equation. {\textcopyright} 2009 Elsevier Inc. All rights reserved.",

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AB - 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 ?. Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn-Hilliard equation. © 2009 Elsevier Inc. All rights reserved.

KW - Cahn-Hilliard equation

KW - Finite elements

KW - Multigrid method

KW - Obstacle free energy

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JF - Applied Mathematics and Computation

SN - 0096-3003

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A multigrid method for the Cahn-Hilliard equation with obstacle potential

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