340 IGPM340.pdf        April 2012
TITLE Analysis of a DG-XFEM Discretization for a Class of Two-Phase Mass Transport Problems
AUTHORS Christoph Lehrenfeld, Arnold Reusken
ABSTRACT 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 DG-XFEM method is new. An error analysis is presented which results in optimal discretization error bounds. Results of numerical experiments are given which illustrate the accuracy of the method
KEYWORDS transport problem, Nitsche method, XFEM, DG space-time finite element method
DOI 10.1137/120875260
PUBLICATION SIAM journal on numerical analysis
51(2), 958-983 (2013)