Fitted finite element discretization of two--phase stokes flow

Abstract

We propose a novel fitted finite element method for two-phase Stokes flow problems that uses piecewise linear finite elements to approximate the moving interface. The method can be shown to be unconditionally stable. Moreover, spherical stationary solutions are captured exactly by the numerical approximation. In addition, the meshes describing the discrete interface in general do not deteriorate in time, which means that in numerical simulations a smoothing or a remeshing of the interface mesh is not necessary. We present several numerical experiments for our numerical method, which demonstrate the accuracy and robustness of the proposed algorithm.