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

DOI10.1007/978-3-0348-0133-1_2zbMath1356.49009OpenAlexW1530637460MaRDI QIDQ2961050

Martin V. Butz, Lavinia Sarbu, Vanessa Styles, Harald Garcke, Luise Blank

Publication date: 17 February 2017

Published in: International Series of Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://epub.uni-regensburg.de/14657/1/MP108.pdf

zbMATH Keywords

optimizationvariational inequalitiesCahn-Hilliard modelphase-field methodAllen-Cahn modelactive set methods

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Methods of quasi-Newton type (90C53) Applications of optimal control and differential games (49N90) Nonlinear parabolic equations (35K55) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for variational inequalities and related problems (65K15)

Related Items

A hybrid FEM for solving the Allen-Cahn equation ⋮ Novel mass-conserving Allen-Cahn equation for the boundedness of an order parameter ⋮ Preconditioning for Allen-Cahn variational inequalities with non-local constraints ⋮ Generalizing Diffuse Interface Methods on Graphs: Nonsmooth Potentials and Hypergraphs ⋮ An adaptive finite element Moreau-Yosida-based solver for a coupled Cahn-Hilliard/Navier-Stokes system ⋮ Optimal Distributed Control of a Nonlocal Convective Cahn--Hilliard Equation by the Velocity in Three Dimensions

Cites Work

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• On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysis
• The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis
• Semi–Smooth Newton Methods for Variational Inequalities of the First Kind
• The Primal-Dual Active Set Strategy as a Semismooth Newton Method

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