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401-4661-00L 6 Credits DR , MSC D-CHAB , D-MAVT , D-MTEC , D-MATH , D-BIOL

Wavelet Solution of Operator Equations

Wavelet FEM for Operator Equations

Lecturers & Examiners: Prof. Dr. Christoph Schwab
VVZ CR n/a

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
  • Wed 14:15-16:00 (HG E 1.1)
  • Thu 13:15-14:00 (HG G 26.5)
3 h weekly

Offered In