eXtended Finite Element Method

The eXtended Finite Element Method (XFEM) have played an increasingly important role to simulate various phenomena, originally mostly in structural mechanics but more recently also in fluid dynamics and in geophysical applications.

These methods have two main characteristics. On the one hand, the ability to add, locally, a priori knowledge about the solution to the approximation space in order  to capture particular features such as discontinuities and singularities present in the solution exactly. On the other hand they allow to handle and to propagate discontinuities and singularities without any re-meshing operation.

XFEM in particular has been used successfully to solve crack initiation and propagation problems, multi-material systems, fluid flow with boundary layers, combustion problems, fluid structure interaction, growth of hydrogels and biofilms among others, with minimal meshing and remeshing of the moving boundaries involved.

The research on XFEM at MOX is mainly focused on the simulation of flows in heterogeneous porous media with complex geometries, in particular in the presence of interfaces such as faults and fractures.

View a list of journal publications and MOX Reports related to XFEM.

View a list of theses related to XFEM.

Pressure in a porous medium crossed by a network of fractures non matching with the underlying grid

Pressure in a porous medium crossed by a network of fractures non matching with the underlying grid

Stokes flow around solid grains. Interfaces are non matching with the grid

Stokes flow around solid grains. Interfaces are non matching with the grid