Chapter

Variational methods for wavelets, with S. Dahlke

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations

Published in print October 2010 | ISBN: 9780199577040
Published online January 2011 | e-ISBN: 9780191595172 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199577040.003.0009

Series: Numerical Mathematics and Scientific Computation

Variational methods for wavelets, with S. Dahlke

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Chapter 9 studies S. Dahlke studies wavelet methods. This is the first presentation in this generality and is appropriate for nonlinear problems and bifurcation for elliptic PDEs. As a consequence of the difficulties with evaluating nonlinear functionals and operators with wavelet arguments, general quasilinear, and fully nonlinear problems are limited, and excluded, respectively. With this exception, the whole spectrum of corresponding wavelet methods is shown to be stable and convergent. Again the corresponding linearized operator has to be boundedly invertible. This chapter finishes with adaptive wavelet methods. In contrast to Chapter 6, nonlinear approximation, and wavelet matrix compression are employed for adaptive descent iterations.

Keywords: wavelet analysis; stable wavelet methods; convergent wavelet methods; bifurcation; elliptic PDEs; adaptive wavelet methods; nonlinear approximation; wavelet matrix compression; adaptive descent iterations; Spectral method; mesh-free methods

Chapter.  15428 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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