## 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