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Mathematics - Analysis | Multiscale Problems and Methods in Numerical Simulations - Lectures given at the C.I.M.E. Summer

Multiscale Problems and Methods in Numerical Simulations

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 9-15, 2001

Bramble, James H., Cohen, Albert, Dahmen, Wolfgang

Canuto, Claudio (Ed.)

2003, XIV, 170 p.

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  • About this book

This volume aims to disseminate a number of new ideas that have emerged in the last few years in the field of numerical simulation, all bearing the common denominator of the "multiscale" or "multilevel" paradigm. This covers the presence of multiple relevant "scales" in a physical phenomenon; the detection and representation of "structures", localized in space or in frequency, in the solution of a mathematical model; the decomposition of a function into "details" that can be organized and accessed in decreasing order of importance; and the iterative solution of systems of linear algebraic equations using "multilevel" decompositions of finite dimensional spaces.

Content Level » Research

Keywords » Finite Elements - Wavelets - adaptive methods - best approximation - finite element method - multigrid methods

Related subjects » Analysis - Computational Science & Engineering

Table of contents 

Preface.- A. Cohen: Theoretical Applied and Computational Aspects of Nonlinear Approximation.- W. Dahmen: Multiscale and Wavelet Methods for Operator Equations.- J. H. Bramble: Multilevel Methods in Finite Elements.

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