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

✍ Scribed by James H. Bramble, Albert Cohen, Wolfgang Dahmen (auth.), Claudio Canuto (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2003
• Tongue: English
• Leaves: 150
• Series: Lecture Notes in Mathematics 1825
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Theoretical, Applied and Computational Aspects of Nonlinear Approximation....Pages 1-29
Multiscale and Wavelet Methods for Operator Equations....Pages 31-96
Multilevel Methods in Finite Elements....Pages 97-151

✦ Subjects

Fourier Analysis; Approximations and Expansions; Numerical Analysis