Multiscale and geometric methods for linear elliptic and parabolic partial differential equations
- In this thesis a variety of linear elliptic and parabolic boundary value probelms with general geometries are investigated. In chapter 3 and chapter 4, we derive a fictitious domain/penalty method for parabolic PDE with Dirichlet and Neumann conditions, got some convergence results and error estimates. In chapter 5, we construct a fictitious domain/successive approximation approach to a variety of BVP and present multigrid algorithms. In chapter 6, a modified wavelet sampling formulae is established and used for a class of anisotropic problems to get a robust fast solver.
| Author: | Shaowu Tang |
|---|---|
| URN: | urn:nbn:de:101:1-201305171104 |
| Referee: | Raymond O. Wells, Marcel Oliver, Götz Pfander, Joachim Vogt, Wolfgang Hiller |
| Advisor: | Raymond O. Wells |
| Document Type: | Doctoral Thesis |
| Language: | English |
| Year of first Publication: | 2005 |
| Publishing Institution: | IRC-Library, Information Resource Center der Jacobs University Bremen |
| Granting Institution: | Jacobs Univ. |
| Date of final exam: | 2005/06/29 |
| Release Date: | 2016/02/03 |
| Tag: | fictitious domain; geometric permutation matrix; penalty method; successive approximation; wavelet-Galerkin method |
| PhD degrees: | Mathematics |
| loc: | Q Science / QA Mathematics (incl. computer science) |
| Schools (for defense dates until 2014): | SES School of Engineering and Science |
