Wavelet adaptive method for second order elliptic problems: boundary conditions and domain decomposition |
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Authors: | A Cohen and R Masson |
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Institution: | (1) Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, tour 55–65, 5ème étage, 4 place Jussieu, 75252 Paris Cedex 05, France; e-mail: cohen@ann.jussieu.fr , FR;(2) Division Informatique, Scientifique et Mathématiques Appliquées, Institut Fran?ais du pétrole, BP 311, 92852 Rueil Malmaison Cedex, France; e-mail: roland.masson@ifp.fr , FR |
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Abstract: | Summary. Wavelet methods allow to combine high order accuracy, multilevel preconditioning techniques and adaptive approximation, in
order to solve efficiently elliptic operator equations. One of the main difficulty in this context is the efficient treatment
of non-homogeneous boundary conditions. In this paper, we propose a strategy that allows to append such conditions in the
setting of space refinement (i.e. adaptive) discretizations of second order problems. Our method is based on the use of compatible
multiscale decompositions for both the domain and its boundary, and on the possibility of characterizing various function
spaces from the numerical properties of these decompositions. In particular, this allows the construction of a lifting operator
which is stable for a certain range of smoothness classes, and preserves the compression of the solution in the wavelet basis.
An explicit construction of the wavelet bases and the lifting is proposed on fairly general domains, based on conforming domain decomposition techniques.
Received November 2, 1998 / Published online April 20, 2000 |
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Keywords: | Mathematics Subject Classification (1991): 65N55 |
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