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   -> Volume 6, Issue 12

Preprint: Element-by-element construction of wavelets...
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Rob Stevenson (

PostPosted: Fri Nov 28, 1997 12:50 pm    
Subject: Preprint: Element-by-element construction of wavelets...
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#6 Preprint: Element-by-element construction of wavelets...

Title: Element-by-element construction of wavelets satisfying
stability and moment conditons

Authors: Wolfgang Dahmen and Rob Stevenson

Abstract: In this paper, we construct a class of locally supported
wavelet bases for C^0 Lagrange finite element spaces on possibly
non-uniform meshes on n-dimensional domains or manifolds. The wavelet
bases are stable in the Sobolev spaces H^s for |s|<3/2 (|s|<=1 on
Lipschitz' manifolds), and the wavelets can be arranged to have, in
principal, any desired number of vanishing moments. As a consequence,
these bases can be used e.g. for constructing an optimal solver of
discretized H^s-elliptic differential- or integral problems for s in
above ranges.

The construction of the wavelets consists of two parts: An implicit
part involves some computations on a reference element which, for each
type of finite element space, have to be performed only once. In
addition there is an explicit part which takes care of the necessary
adaptations of the wavelets to the actual mesh. The only condition we
need for this construction to work is that the refinements of initial
elements are uniform.

We will show that the wavelet bases can be implemented efficiently.

A copy can be downloaded from

or can be obtained by emailing the authors
( or
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