Blank, Luise and Garcke, Harald and Sarbu, Lavinia and Styles, Vanessa
Non-local Allen-Cahn systems: Analysis and a primal dual active set method.
Preprintreihe der Fakultät Mathematik 2/2011,
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|
|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|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||18 Apr 2011 07:00|
|Last Modified:||21 Jul 2011 02:11|