A Monolithic Arbitrary Lagrangian-Eulerian Finite Element Analysis for a Stokes/Parabolic Moving Interface Problem

In this paper, an arbitrary Lagrangian-Eulerian (ALE)-finite element method (FEM) is developed within the monolithic approach for a moving-interface model problem of a transient Stokes/parabolic coupling with jump coefficients-a linearized fluid-structure interaction (FSI) problem. A new H-1-projection is defined for this problem for the first time to account for the mesh motion due to the moving interface. The well-posedness and optimal convergence properties in both the energy norm and L-2 norm are analyzed for this mixed-type H-1-projection, with which the stability and optimal error estimate in the energy norm are derived for both semi- and fully discrete mixed finite element approximations to the Stokes/parabolic interface problem. Numerical experiments are carried out to validate all theoretical results. The developed analytical approach can be extended to a general FSI problem.