Allen-Cahn and Cahn-Hilliard Variational Inequalities Solved with Optimization Techniques

  • Luise BlankEmail author
  • Martin Butz
  • Harald Garcke
  • Lavinia Sarbu
  • Vanessa Styles
Part of the International Series of Numerical Mathematics book series (ISNM, volume 160)


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.


Optimization Phase-field method Allen-Cahn model Cahn-Hilliard model variational inequalities active set methods 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Luise Blank
    • 1
    Email author
  • Martin Butz
    • 1
  • Harald Garcke
    • 1
  • Lavinia Sarbu
    • 2
  • Vanessa Styles
    • 2
  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  2. 2.Department of MathematicsUniversity of SussexBrightonUK

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