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Non-local Allen-Cahn systems: Analysis and a primal dual active set method
Blank, Luise, Garcke, Harald, 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 (Unpublished)Date of publication of this fulltext: 18 Apr 2011 07:00
Monograph
DOI to cite this document: 10.5283/epub.20502
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 ...
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.
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Details
| Item type | Monograph (Working Paper) | ||||||||||||||
| Series of the University of Regensburg: | Preprintreihe der Fakultät Mathematik | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Volume: | 2/2011 | ||||||||||||||
| Date | 2011 | ||||||||||||||
| Institutions | Mathematics > Prof. Dr. Harald Garcke | ||||||||||||||
| Classification |
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| Keywords | Allen-Cahn systems, non-local constraints, variational inequality, vector-valued obstacle problems, primal-dual active set method, semi-smooth Newton method | ||||||||||||||
| Dewey Decimal Classification | 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| Status | Unpublished | ||||||||||||||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 | ||||||||||||||
| URN of the UB Regensburg | urn:nbn:de:bvb:355-epub-205022 | ||||||||||||||
| Item ID | 20502 |
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