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

journal contribution
posted on 2023-06-08, 12:37 authored by Luise Blank, Harald Garcke, Lavinia Sarbu, Vanessa StylesVanessa Styles
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. The local convergence behaviour of the primal-dual active set algorithm is studied by interpreting the approach as a semi-smooth Newton method and numerical simulations are presented demonstrating its efficiency.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

IMA Journal of Numerical Analysis

ISSN

0272-4979

Publisher

Oxford University Press

Issue

4

Volume

33

Page range

1126-1155

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2013-03-08

First Open Access (FOA) Date

2013-03-08

First Compliant Deposit (FCD) Date

2012-10-17

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