Fifth Mississippi State Conference on Differential Equations and
Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2002, pp. 211225.
A wavelet Galerkin method applied to partial differential
equations with variable coefficients
Jose Roberto Linhares de Mattos & Ernesto Prado Lopes
Abstract:
We consider the problem
,
,
,
where
is bounded below by a positive constant.
The solution on the boundary
is a known function
and
.
This is an illposed problem in the sense
that a small disturbance on the boundary specification
,
can produce a big alteration on its solution, if it exists.
We consider the existence of a solution
and we use a wavelet Galerkin method with the Meyer multiresolution analysis,
to filter away the highfrequencies and to obtain wellposed approximating
problems in the scaling spaces
.
We also derive an estimate for
the difference between the exact solution of the problem and the orthogonal
projection, onto
,
of the solution of the approximating problem
defined in
.
Published February 28, 2003.
Subject classifications: 65T60.
Key words: Wavelet, multiresolution analysis.
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Jose Roberto Linhares de Mattos
Federal University Fluminense
Institute of Mathematics, Department of Geometry
Rua Mario Santos Braga, s/n, Campus do Valonguinho
Niteroi, RJ, CEP 24020140, Brazil
email: jrlinhares@vm.uff.br


Ernesto Prado Lopes
Federal University of Rio de Janeiro
COPPE, Systems and Computing Engineering Program
Tecnology Center, Bloco H
and
Institute of Mathematics, Tecnology Center, Bloco C
Ilha do Fundao,
Rio de Janeiro RJ, CEP 21945970, Brazil
email: lopes@cos.ufrj.br

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