A novel arbitrary Lagrangian–Eulerian finite element method for a parabolic/mixed parabolic moving interface problem

In this paper, a monolithic arbitrary Lagrangian–Eulerian (ALE)-finite element method (FEM) is developed based upon novel ALE mapping for type of parabolic/mixed parabolic moving interface problem with jump coefficients. A stable Stokes-pair mixed FEM within specific stabilization technique and time-difference scheme are to discretize in both semi- fully discrete fashion, which the stability error estimate analyses conducted frame. Numerical experiments carried out validate all theoretical results different cases. The ALE-FEM can be extended that involves pore fluid (Darcy) equation or Biot’s model future.