Primal-dual active set methods for Allen-Cahn variational inequalities with nonlocal constraints

We propose and analyze a primal‐dual active set method for discretized versions of the local and nonlocal Allen–Cahn variational inequalities. An existence result for the nonlocal variational inequality is shown in a formulation involving Lagrange multipliers for local and nonlocal constraints. Loca...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2013-05, Vol.29 (3), p.999-1030
Main Authors: Blank, Luise, Garcke, Harald, Sarbu, Lavinia, Styles, Vanessa
Format: Article
Language:English
Subjects:
Allen-Cahn variational inequality
Computational efficiency
Computer simulation
Convergence
finite element approximation
Inequalities
Lagrange multipliers
Mathematical models
Newton methods
nonlocal constraints
Numerical analysis
primal-dual active set methods
semismooth Newton methods
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Summary:We propose and analyze a primal‐dual active set method for discretized versions of the local and nonlocal Allen–Cahn variational inequalities. An existence result for the nonlocal variational inequality is shown in a formulation involving Lagrange multipliers for local and nonlocal constraints. Local convergence of the discrete method is shown by interpreting the approach as a semismooth Newton method. Properties of the method are discussed and several numerical simulations demonstrate its efficiency. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
ISSN:0749-159X
1098-2426
DOI:10.1002/num.21742