Mimetic Finite Difference Methods

The mimetic finite difference method (MFD) has become a very popular numerical approach to successfully solve a wide range of problems. This is undoubtedly connected to its great flexibility in dealing with very general polygonal/polyhedral meshes and its capability of preserving the fundamental properties of the underlying physical and mathematical models. The MFD method has been applied with success to a wide range of linear as well non-linear problems. Recently, the mimetic approach has been recasted as the virtual element method (VEM). The research at MOX  in this context, focuses on both the theoretical/computational approximation properties of MFD methods as well as the application of MFD methods to the model flows in fractured porous media.

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

View a list of theses related to MFD methods.

MFD solution of an elliptic problem

MFD solution of an elliptic problem

 

MFD solution of an elliptic obstacle problem

MFD solution of an elliptic obstacle problem