Jose Roberto Linhares de Mattos & Ernesto Prado Lopes
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 ill-posed 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 multi-resolution analysis, to filter away the high-frequencies and to obtain well-posed 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, multi-resolution analysis.
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Note: The authors were nitially posted in reversed.
| 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 24020-140, Brazil
| Ernesto Prado Lopes |
Federal University of Rio de Janeiro
COPPE, Systems and Computing Engineering Program
Tecnology Center, Bloco H
Institute of Mathematics, Tecnology Center, Bloco C
Ilha do Fundao, Rio de Janeiro RJ, CEP 21945-970, Brazil
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