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Wavelet Methods for Elliptic Partial Differential Equations$
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Karsten Urban

Print publication date: 2008

Print ISBN-13: 9780198526056

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780198526056.001.0001

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Wavelets on General Domains

Wavelets on General Domains

(p.257) 8 Wavelets on General Domains
Wavelet Methods for Elliptic Partial Differential Equations

Karsten Urban

Oxford University Press

The construction of wavelets on general domains is performed in three steps. This chapter starts by introducing the construction of scaling functions and wavelets on bounded univariate intervals. Next, building tensor products allows constructing wavelets on rectangular domains. Finally, the Wavelet Element Method (WEM) is introduced. Using non-overlapping domain decomposition and mapping to the unit cube the WEM matches scaling functions and wavelets across the interfaces of the subdomains in order to obtain a globally continuous basis. The realization of the construction in terms of software is shown as well how to use this software.

Keywords:   wavelets on the interval, Wavelet Element Method, tensor product, refinement matrices, norm equivalences

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