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

被引：26

作者：

Blank, Luise ^{[1
]}

Garcke, Harald ^{[1
]}

Sarbu, Lavinia ^{[2
]}

Styles, Vanessa ^{[2
]}

机构：

[1] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

[2] Univ Sussex, Dept Math, Brighton BN1 9RF, E Sussex, England

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2013年 / 29卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

AllenCahn variational inequality; finite element approximation; nonlocal constraints; primal-dual active set methods; semismooth Newton methods; FINITE-ELEMENT APPROXIMATION; TOPOLOGY OPTIMIZATION; OBSTACLE PROBLEM; DIFFUSION; MODEL; EQUATIONS; STRATEGY; STRESS; MOTION; LIQUID;

D O I：

10.1002/num.21742

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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

引用

页码：999 / 1030

页数：32

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