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Wavelet Methods for Elliptic Partial Differential Equations$
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Karsten Urban

Print publication date: 2008

Print ISBN-13: 9780198526056

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780198526056.001.0001

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Multiresolution Galerkin Methods

Multiresolution Galerkin Methods

(p.87) 4 Multiresolution Galerkin Methods
Wavelet Methods for Elliptic Partial Differential Equations

Karsten Urban

Oxford University Press

This chapter uses a Multiresoultion Analysis for the discretization of elliptic boundary value problems. The error analysis is provided and the setup of the linear system of equations is described. Two numerical schemes for solving these linear systems are introduced, namely the BPX-preconditioner and multigrid. Several numerical comparisons are shown.

Keywords:   multiresolution analysis, Bramble-Hilbert lemma, BPX-preconditioner, multigrid, scaling functions, refinable integrals

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