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Wavelet Methods for Elliptic Partial Differential Equations

Karsten Urban

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.001.0001
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Wavelets have become a powerful tool in several applications by now. Their use for the numerical solution of operator equations has been investigated more recently. By now the theoretical ... More


Wavelets

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0005
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Starting from a Multiresolution Analysis, wavelets are introduced as a basis for the corresponding detail spaces. The main families are introduced, namely orthogonal Daubechies' wavelets as well as ... More


Variational methods for wavelets, with S. Dahlke

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 9 studies S. Dahlke studies wavelet methods. This is the first presentation in this generality and is appropriate for nonlinear problems and bifurcation for elliptic PDEs. As a consequence of ... More


Wavelet-Galerkin Methods

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0006
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Using wavelets as basis for the test and trial spaces of a Galerkin method allows an optimal preconditioning of the stiffness matrix. It is proven that a diagonal scaling provides such a ... More


Wavelets on General Domains

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0008
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

The construction of wavelets on general domains is performed in three steps. This chapter starts by introducing the construction of scaling functions and wavelets on bounded univariate intervals. ... More


Introduction

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0001
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

This chapter gives an outline of the history of wavelets, in particular with respect to their use to numerically solve partial differential equations. The scope of the book and its outline is ... More


Adaptive Wavelet Methods

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0007
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

This chapter starts by adaptively approximating a given function and introduce the main theoretical concepts. After describing the more classical approach to adaptivity based upon a-posteriori error ... More


Some Applications

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0009
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Some recent applications of wavelet methods are shown. The chapter starts with the numerical realization of the WEM and consider the L-shaped domain as a model for a non-separable domain. The chapter ... More


Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Klaus Boehmer

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, and create an exciting interplay. Other books discuss nonlinearity by a very few important ... More


Transformation, convolution, and correlation

Bernhard Blümich

in NMR Imaging of Materials

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198526766
eISBN:
9780191709524
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526766.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

Transformation, convolution, and correlation are used over and over again in nuclear magnetic resonance (NMR) spectroscopy and imaging in different contexts and sometimes with different meanings. The ... More


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