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Type: Artigo de periódico
Title: Convergence Estimates For The Wavelet-galerkin Method: Superconvergence At The Node Points
Author: Gomes S.M.
Abstract: In this paper we consider a regular 1-periodic initial value problem and Galerkin approximate solutions in subspaces νt spanned by scaled translates of a basic function φ{symbol}. Our goal is to estimate the error when φ{symbol} is in a class of functions which we name[Figure not available: see fulltext.]. Here r is a regularity parameter and m is related with a property (the Strang and Fix condition) which determines the best order of accuracy in the L2-norm of approximations from νh. When m=r,[Figure not available: see fulltext.] includes all scaling functions corresponding to r-regular multiresolution analyses of L2(ℝ). We get the exact node values of the given initial condition as coefficients for the approximate initial data. With this procedure, the coefficients of the resulting Galerkin solution can give a very accurate approximation of the exact solution at the node points, provided that φ{symbol} has many vanishing moments. Since this property is not satisfied in general, we work with another modified basic function φ{symbol}* constructed from the integer translates of φ{symbol}. Global L2-estimates are also obtained. © 1995 J.C. Baltzer AG, Science Publishers.
Rights: fechado
Identifier DOI: 10.1007/BF03177516
Date Issue: 1995
Appears in Collections:Unicamp - Artigos e Outros Documentos

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