Abstract
We show the existence and uniqueness of a solution for the nonlocal vector-valued Allen-Cahn variational inequality in a formulation involving Lagrange multipliers for local and nonlocal constraints. Furthermore, we propose and analyse a primal-dual active set (PDAS) method for local and nonlocal vector-valued Allen-Cahn variational inequalities. The local convergence behaviour of the PDAS ...
Abstract
We show the existence and uniqueness of a solution for the nonlocal vector-valued Allen-Cahn variational inequality in a formulation involving Lagrange multipliers for local and nonlocal constraints. Furthermore, we propose and analyse a primal-dual active set (PDAS) method for local and nonlocal vector-valued Allen-Cahn variational inequalities. The local convergence behaviour of the PDAS algorithm is studied by interpreting the approach as a semismooth Newton method and numerical simulations are presented demonstrating its efficiency.
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