Nonlocal Allen-Cahn systems. Analysis and a primal-dual active set method (Q2856615)

The Allen-Cahn systems describe the capillarity-driven interface evolution with mass conservation. The authors reformulate the system with the help of Lagrange multipliers. The existence and uniqueness of a solution is shown. A primal-dual active set method is introduced and applied to a finite element discretization of an implicit Euler discretization of the system. The method is analysed by reformulating it as a semismooth Newton method. Some computational results are presented to show how the method iteration numbers change if time and spatial discretization parameters are decreased simultaneously. Solutions are computed for the volume-constrained case in three space dimensions.