Workshop on Foundations of Numerical PDEs

July 7 - July 9, 2005

Universidad de Cantabria in Santander, Spain

Mimetic Finite Differences Methods for Diffusion Problems

Franco Brezzi

Dipartimento di Matematica at Università di Pavia

Abstract:   The talk will overview the basic features of Mimetic Finite Difference Methods, taking as a model problem Darcy's law for filtration in porous media. After a rather general presentation, we will concentrate on the basic ideas that allowed the extension of the method to a very wide class of geometrical situations, including polyhedra with curved faces. This last part will be based on several papers written in collaboration with K. Lipnikov and M. Shashkov from Los Alamos N.L. and V. Simoncini from the University of Bologna.