The Arbitrary Lagrangian-Eulerian Finite Element Method for a Transient Stokes/Parabolic Interface Problem

Abstract

In this paper, a type of nonconservative arbitrary Lagrangian-Eulerian (ALE) finite element method is developed and analyzed in the monolithic frame for a transient Stokes/parabolic moving interface problem with jump coefficients. The mixed and the standard finite element approximations are adopted for the transient Stokes equations and the parabolic equation on either side of the moving interface, respectively. The stability and optimal convergence properties of both semi- and full discretizations are analyzed in terms of the energy norm. The developed numerical method can be generally extended to the realistic fluid-structure interaction (FSI) problems in a time-dependent domain with a moving interface.