Adaptive finite element methods for Cahn-Hilliard equations

Authors:
L'ubomír Baňas;Robert Nürnberg
Affiliations:
Department of Mathematics, Imperial College, London SW7 2AZ, UK;Department of Mathematics, Imperial College, London SW7 2AZ, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 1
Cited 2

Efficient and Reliable A Posteriori Error Estimators for Elliptic Obstacle Problems

SIAM Journal on Numerical Analysis

Distributed Optimal Control of the Cahn-Hilliard System Including the Case of a Double-Obstacle Homogeneous Free Energy Density

SIAM Journal on Control and Optimization
A conservative numerical method for the Cahn-Hilliard equation with Dirichlet boundary conditions in complex domains

Computers & Mathematics with Applications

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Abstract

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.