Section: New Results

Finite element methods for interface problems

Participants : Nelly Barrau, Roland Becker, Robert Luce, Erik Burman, Peter Hansbo.

The original formulation of NXFEM [62] is based on the doubling of elements. In some situations, as the case of a moving interface, it is computationally more convenient to have a method with local enrichment, as for the standard XFEM. In [41] we have developed such an approach based on NXFEM. We have developed an hierarchical formulation for a fictitious domain formulation in [13]

One of the technical difficulties is the simultaneous robustness of the method with respect to the size of the intersection of a mesh cell with the interface and with respect to the discontinuous diffusion parameters. This is the subject of the thesis of Nelly Barrau, supervised by Robert Luce and Eric Dubach (LMAP).