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Wavelet Solution of Operator Equations
Wavelet FEM for Operator Equations
Last Updated: 2026-02-05 15:06:38
Abstract
Review of Spline Wavelet Methods for the numerical solution of Elliptic Operator EquationsApplications to Stochastic PDE, Integrodifferential Equations and PDEs in high dimensionaldomains.
Content
Strongly Elliptic Operator Equations. Galerkin Discretization. Construction of Spline Wavelet Finite Elements. Wavelet norm equivalences in Sobolev and Besov Spaces. Linear and nonlinear Approximation; Best N-Term and Adapitive Approximation. General Framework for adaptive numerical approximation of operator equations of Cohen. Dahmen, DeVore. Besov Spaces and Wavelet Bases in Tensorized Domains. Adaptive Sparse Grids. Applications: Adaptive Solution of Operator Equations with stochastic data, Discretization of SPDEs, Adaptive Solution of Equations in high-dimensional domains (Chemistry, Finance, Radiation Transport and Multiscale/ Homogenization Problems in Engineering). Implementational Aspects: Tree-encoding, Adaptive Quadrature, Matrix Compressions.
Resources
Lecture Notes
There will be no Skript -- Material will be based on the text and on recent research articles.
Literature
A. Cohen: The Numerical Analysis of Wavelet Methods, Elsevier 2003. Various recent (2003-2006) Research articles will be made available for the course.
General Information
- Language
- English
- Levels
- DR , MSC
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Wavelet FEM for Operator Equations |
|
3 h weekly |