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   -> Volume 6, Issue 7


Preprint: Preprint by Canuto, Tabacco and Urban
 
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Karsten Urban (urban@igpm.rwth-aachen.de)
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PostPosted: Mon Jun 16, 1997 5:14 pm    
Subject: Preprint: Preprint by Canuto, Tabacco and Urban
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#1 Preprint: Preprint by Canuto, Tabacco and Urban

The following preprint is available

"The Wavelet Element Method, Part I: Construction and Analysis"
by
Claudio Canuto, Anita Tabacco and Karsten Urban

under the following sites:

By anonymous ftp:

site : ftp.igpm.rwth-aachen.de
directory: pub/urban/reports
filename : wem.ps.Z (compressed PostScript file)

By netscape/Mosaic:

ftp://www.igpm.rwth-aachen.de/pub/urban/reports/wem.ps.Z

Abstract:

The Wavelet Element Method (WEM) combines biorthogonal wavelet systems
with the philosophy of Spectral Element Methods in order to obtain a
biorthogonal wavelet system on fairly general bounded domains in some
$er^n$. The domain of interest is split into subdomains which are
mapped to a simple reference domain, here $n$--dimensional cubes.
Thus, one has to construct appropriate biorthogonal wavelets on the
reference domain such that mapping them to each subdomain and matching
along the interfaces leads to a wavelet system on the domain.

In this paper we use adapted biorthogonal wavelet systems on the
interval in such a way, that tensor products of these functions can be
used for the construction of wavelet bases on the reference domain. We
describe the matching procedure in any dimension $n$ in order to
impose continuity and prove that it leads to a construction of a
biorthogonal wavelet system on the domain. These wavelet systems
characterize Sobolev spaces measuring both piecewise and global
regularity. The construction is detailed for a bivariate example and
an application to the numerical solution of second order partial
differential equations is given.
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