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Non-local Allen-Cahn systems: Analysis and a primal dual active set method

Blank, Luise and Garcke, Harald and Sarbu, Lavinia and Styles, Vanessa (2011) Non-local Allen-Cahn systems: Analysis and a primal dual active set method. Preprintreihe der Fakultät Mathematik 2/2011, Working Paper. (Unpublished)

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Abstract

We show existence and uniqueness of a solution for the non-local vector-valued Allen-Cahn variational inequality in a formulation involving Lagrange multipliers for local and non-local constraints. Furthermore, we propose and analyze
a primal-dual active set method for local and non-local vector-valued Allen-Cahn variational inequalities. Convergence of the primal-dual active set algorithm is shown by interpreting the approach as a semi-smooth Newton method and numerical simulations are presented demonstrating its efficiency.

Item Type:

Monograph (Working Paper)

Institutions:

Mathematics > Prof. Dr. Harald Garcke

Classification:

Notation	Type
35K55	MSC
65K10	MSC
90C33	MSC
90C53	MSC
82C24	MSC
65M60	MSC

Keywords:

Allen-Cahn systems, non-local constraints, variational inequality, vector-valued obstacle problems, primal-dual active set method, semi-smooth Newton method

Subjects:

500 Science > 510 Mathematics

Status:

Unpublished

Refereed:

No, this version has not been refereed yet (as with preprints)

Created at the University of Regensburg:

Yes

Owner:

Eva Ruetz

Deposited On:

18 Apr 2011 09:00