A Nitsche‐based cut finite element solver for two‐phase Stefan problems

Abstract

We present a cut finite element method based on ghost penalty stabilization technique for solving two‐phase Stefan problems. The essential interfacial constraints are weakly enforced using the symmetric variant of Nitsche's method. To track the interface efficiently, the level‐set technique is employed and the front location is updated at each time step by solving a transport equation. Because this is a convection problem, we utilize the continuous interior penalty method to stabilize the finite element formulation. According to the Stefan condition, the normal velocity of the interface is proportional to the jump in the interfacial flux. To accurately approximate this quantity, we use a recent post‐processing technique that combines a ghost penalty regularization and the domain integral method on cut elements. We validate our algorithm with several numerical examples that demonstrate optimal convergence.