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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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Elliptic Boundary Value Problems

Elliptic Boundary Value Problems

(p.63) 3 Elliptic Boundary Value Problems
Wavelet Methods for Elliptic Partial Differential Equations

Karsten Urban

Oxford University Press

A model problem is introduced, namely the univariate two-point boundary value problem, both with periodic boundary conditions and homogeneous Dirichlet boundary conditions. The chapter describes the variational formulation, regularity theory and a numerical discretization in terms of Galerkin methods.

Keywords:   two-point boundary value problem, variational formulation, Galerkin methods, Lax-Milgram theorem, Sobolev spaces

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