Graduate Seminar "Aktuelle Themen der Numerik"

 

Thursday, Nov 21, 2013, 02:00 pm

The Nitsche XFEM-DG Space-Time Method for Two-Phase Mass Transport Problems in Three Space Dimensions

Dipl.-Ing. Christoph Lehrenfeld (IGPM, RWTH Aachen)

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 a new finite element discretization method for this mass transport problem which has been introduced and analyzed in [1].  This method is based on a  space-time  approach  in which  a  discontinuous  Galerkin  (DG) technique (in time) is combined with an extended finite element method (XFEM). The jump condition is satisfied in a weak sense by using the Nitsche method. For an implementation of the method we have to evaluate integrals on the space-time subdomains. In the spatially three dimensional case that means dealing with four-dimensional geometries which are typically given only implicitly as the zero-level of a level-set function. In [2] a strategy for the approximation of the space-time interface and the space-time subdomains is presented. A crucial ingredient within this strategy is a new method for dividing four-dimensional prisms intersected by a piecewise planar space-time interface into simplices. The strategy is explained and corresponding numerical studies are presented and discussed.

References:
[1]  A. Reusken and C. Lehrenfeld, Analysis of a Nitsche XFEM-DG Discretization for a class of Two-Phase
Mass Transport Problems. SIAM J. Numer. Anal., 51:958–983, 2013.
[2]  C. Lehrenfeld, The Nitsche XFEM-DG Space-Time Method and its Implementation in Three Space Dimensions,  submitted to SIAM J. Sci. Comp., 2013.

Time: 02:00 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen