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Published in:
2012 | OriginalPaper | Chapter
Allen-Cahn and Cahn-Hilliard Variational Inequalities Solved with Optimization Techniques
Authors : Luise Blank, Martin Butz, Harald Garcke, Lavinia Sarbu, Vanessa Styles
Published in: Constrained Optimization and Optimal Control for Partial Differential Equations
Publisher: Springer Basel
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Parabolic variational inequalities of Allen-Cahn and Cahn-Hilliard type are solved using methods involving constrained optimization. Time discrete variants are formulated with the help of Lagrange multipliers for local and non-local equality and inequality constraints. Fully discrete problems resulting from finite element discretizations in space are solved with the help of a primal-dual active set approach. We show several numerical computations also involving systems of parabolic variational inequalities.