Multiscale Wavelet Methods for Partial Differential Equations

Wolfgang Dahmen, Andrew J. Kurdila and Peter Oswald (Eds.)0122006755, 9780122006753, 9780080537146

This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource. Key Features * Covers important areas of computational mechanics such as elasticity and computational fluid dynamics * Includes a clear study of turbulence modeling * Contains recent research on multiresolution analyses with operator-adapted wavelet discretizations * Presents well-documented numerical experiments connected with the development of algorithms, useful in specific applications

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Table of contents :
Content:
Preface
Pages vii-x
Wolfgang Dahmen, Andrew J. Kurdila, Peter Oswald

Contributors
Pages xi-xiv

Multilevel solvers for elliptic problems on domains Original Research Article
Pages 3-58
Peter Oswald

Wavelet-like methods in the design of efficient multilevel preconditioners for elliptic PDEs Original Research Article
Pages 59-105
Panayot S. Vassilevski, Junping Wang

An adaptive collocation method based on interpolating wavelets Original Research Article
Pages 109-135
Silvia Bertoluzza

An adaptive pseudo-wavelet approach for solving nonlinear partial differential equations Original Research Article
Pages 137-197
Gregory Beylkin, James M. Keiser

A dynamical adaptive concept based on wavelet packet best bases: Application to convection diffusion partial differential equations Original Research Article
Pages 199-235
Pascal Joly, Yvon Maday, Valérie Perrier

Nonlinear approximation and adaptive techniques for solving elliptic operator equations Original Research Article
Pages 237-283
Stephan Dahlke, Wolfgang Dahmen, Ronald A. DeVore

Fully discrete multiscale galerkin BEM Original Research Article
Pages 287-346
Tobias von Petersdorff, Christoph Schwab

Wavelet multilevel solvers for linear Ill-posed problems stabilized by Tikhonov regularization Original Research Article
Pages 347-380
Andreas Rieder

Towards object oriented software tools for numerical multiscale methods for PDEs using wavelets Original Research Article
Pages 383-412
Titus Barsch, Karsten Urban, Angela Kunoth

Scaling function and wavelet preconditioners for second order elliptic problems Original Research Article
Pages 413-438
Jeonghwan Ko, Andrew J. Kurdila, Peter Oswald

Local models and large scale statistics of the kuramoto–sivashinsky equation Original Research Article
Pages 441-471
Juan Elezgaray, Gal Berkooz, Harry Dankowicz, Philip Holmes, Mark Myers

Theoretical dimension and the complexity of simulated turbulence Original Research Article
Pages 473-492
Mladen Victor Wickerhauser, Marie Farge, Eric Goirand

Analysis of second order elliptic operators without boundary conditions and with VMO or Hölderian coefficients Original Research Article
Pages 495-539
J.M. Angeletti, S. Mazet, P. Tchamitchian

Some directional elliptic regularity for domains with cusps Original Research Article
Pages 541-565
Matthias Holschneider

Subject index
Pages 567-570