Blank, Luise and Garcke, Harald and Sarbu, Lavinia and Styles, Vanessa (2013) Primal-dual active set methods for Allen-Cahn variational inequalities with nonlocal constraints. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 29 (3). pp. 999-1030. ISSN 0749-159X,
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We propose and analyze a primal-dual active set method for discretized versions of the local and nonlocal AllenCahn 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. (c) 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT APPROXIMATION; POINTWISE STATE CONSTRAINTS; MEAN-CURVATURE FLOW; TOPOLOGY OPTIMIZATION; OBSTACLE PROBLEM; NEWTON METHOD; MODEL; EQUATIONS; DIFFUSION; SIMULATIONS; AllenCahn variational inequality; finite element approximation; nonlocal constraints; primal-dual active set methods; semismooth Newton methods |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 16 Apr 2020 07:43 |
| Last Modified: | 16 Apr 2020 07:43 |
| URI: | https://pred.uni-regensburg.de/id/eprint/16786 |
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