Plenary and Semi-Plenary Lectures
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| Title: |
| Mimetic Finite Differences Methods |
| Lecturer: |
| Franco Brezzi |
| Abstract: |
The Mimetic Finite Difference Method (MFDM) is a rather recent approach that could be classified, roughly speaking, in between Mixed Finite Element Methods and Finite Volumes.
At the moment, the main advantage of MFDM consists in the easier treatment of very complex geometrical situations, including general polyhedral elements with curved faces, which can occur, for instance, when dealing with heterogeneous materi- als having a geometrically complicated substructure, or during the coarsening phase of a self-adaptive decomposition process.
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 constitute the back- bone of the method, and discuss the main underlying mathematical structures. We shall also present some recent numerical tricks that make the implementation easier and cheaper.
The talk is mostly based on several papers written in collaboration with K. Lip- nikov and M. Shashkov from Los Alamos N.L. and V. Simoncini from the University of Bologna. |
 Franco Brezzi was born near Milano (Italy) in 1945. He graduated in Mathematics at the University of Pavia in 1967, and in 1975 became full professor of Mathematical Analysis (first in Torino, and then back in Pavia).
He has been the Director of the Institute of Applied Mathematics of the Pavia University from 1977 to 1981 and Director of the Department of Structural Mechanics of the Pavia University from 1983 to 1986.
He is currently Professor of Mathematical Analysis at the Engineering Faculty of the Pavia University, and Director of IMATI (Institute of Applied Mathematics and Information Technologies) of Italian CNR (National Council of Researches).
He is Managing Editor of Mathematical Models & Methods in Applied Sciences, Editor-in-Chief of Numerische Mathematik, and member of the Editorial Board of about 25 international journals and Book Series. He is also member of the Istituto Lombardo - Accademia di Scienze e Lettere, and corresponding member of the Accademia Nazionale dei Lincei.
He received several awards, including Premio Citta` di Cagliari, IACM Fellowship, and
IACM Gauss-Newton Medal.
He works mainly in numerical approximation of PDE problems with application to various Engineering fields, as Continuum Mechanics, Fluid Mechanics and Electromagnetics. |
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