Mathematik Primal-dual active set methods for Allen-Cahn variational inequalities with non-local constraints

We propose and analyze a primal-dual active set method for local and nonlocal Allen-Cahn variational inequalities. An existence result for the non-local variational inequality is shown in a formulation involving Lagrange multipliers for local and non-local constraints. Superlinear local convergence is shown by interpreting the approach as a semi-smooth Newton method. Properties of the method are discussed and several numerical simulations demonstrate its efficiency.

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