Abstract
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.
Mathematics Subject Classification (2000). 35K55, 35S85, 65K10, 90C33, 90C53, 49N90, 65M60.
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Blank, L., Butz, M., Garcke, H., Sarbu, L., Styles, V. (2012). Allen-Cahn and Cahn-Hilliard Variational Inequalities Solved with Optimization Techniques. In: Leugering, G., et al. Constrained Optimization and Optimal Control for Partial Differential Equations. International Series of Numerical Mathematics, vol 160. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0133-1_2
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DOI: https://doi.org/10.1007/978-3-0348-0133-1_2
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