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Adaptive Wavelet Methods

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Multiscale and Adaptivity: Modeling, Numerics and Applications

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2040))

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Abstract

Wavelet bases, initially introduced as a tool for signal and image processing, have rapidly obtained recognition in many different application fields. In this lecture notes we will describe some of the interesting properties that such functions display and we will illustrate how such properties (and in particular the simultaneous good localization of the basis functions in both space and frequency) allow to devise several adaptive solution strategies for partial differential equations.While some of such strategies are based mostly on heuristic arguments, for some other a complete rigorous justification and analysis of convergence and computational complexity is available.

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Authors and Affiliations

  1. Istituto di Matematica Applicata e Tecnologie Informatiche del CNR, v. Ferrata 1, Pavia, Italy

    Silvia Bertoluzza

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  1. Silvia Bertoluzza
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Correspondence to Silvia Bertoluzza .

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Bertoluzza, S. (2011). Adaptive Wavelet Methods. In: Multiscale and Adaptivity: Modeling, Numerics and Applications. Lecture Notes in Mathematics(), vol 2040. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24079-9_1

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