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We investigate novel fitted finite element approximations for two-phaseNavier--Stokes flow. In particular, we consider both Eulerian and ArbitraryLagrangian--Eulerian (ALE) finite element formulations. The moving interface isapproximated with the help of parametric piecewise linear finite elementfunctions. The bulk mesh is fitted to the interface approximation, so thatstandard bulk finite element spaces can be used throughout. The meshesdescribing the discrete interface in general do not deteriorate in time, whichmeans that in numerical simulations a smoothing or a remeshing of the interfacemesh is not necessary. We present several numerical experiments, includingconvergence experiments and benchmark computations, for the introducednumerical methods, which demonstrate the accuracy and robustness of theproposed algorithms. We also compare the accuracy and efficiency of theEulerian and ALE formulations.

Fitted front tracking methods for two-phase incompressible Navier--Stokes flow: Eulerian and ALE finite element discretizations