Analysis of a Nitsche XFEM-DG Discretization for a Class of Two-Phase Mass Transport Problems

We consider a standard model for mass transport across an evolving interface. The solution has to satisfy a jump condition across an evolving interface. We present and analyze a finite element discretization method for this mass transport problem. This method is based on a space-time approach in which a discontinuous Galerkin (DG) technique is combined with an extended finite element method (XFEM). The jump condition is satisfied in a weak sense by using the Nitsche method. This Nitsche XFEM-DGmethod is new. An error analysis is presented. Results of numerical experiments are given which illustrate the accuracy of the method.