A cut finite element method for a Stokes interface problem

TL;DR

This paper introduces a cut finite element method for solving Stokes interface problems involving two immiscible fluids, allowing for non-aligned interfaces and ensuring stability and optimal error estimates.

Contribution

It proposes a Nitsche-based formulation with stabilization that handles non-conforming interfaces and guarantees well-conditioned matrices regardless of interface position.

Findings

Achieves optimal a priori error estimates.

Ensures well-conditioned stiffness matrices.

Handles non-aligned fluid interfaces effectively.

Abstract

We present a finite element method for the Stokes equations involving two immiscible incompressible fluids with different viscosities and with surface tension. The interface separating the two fluids does not need to align with the mesh. We propose a Nitsche formulation which allows for discontinuities along the interface with optimal a priori error estimates. A stabilization procedure is included which ensures that the method produces a well conditioned stiffness matrix independent of the location of the interface.