Multiscale Problems and Methods in Numerical Simulations [electronic resource] : Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 9-15, 2001 / by James H. Bramble, Albert Cohen, Wolfgang Dahmen ; edited by Claudio Canuto.

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.

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.