TY  - THES
U1  - Dissertation oder Habilitation
A1  - Tang, Shaowu
T1  - Multiscale and geometric methods for linear elliptic and parabolic partial differential equations
N2  - 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.
AB  - 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.
KW  - wavelet-Galerkin method
KW  - fictitious domain
KW  - penalty method
KW  - successive approximation
KW  - geometric permutation matrix
Y1  - 2005
U6  - https://nbn-resolving.org/urn:nbn:de:101:1-201305171104
UN  - https://nbn-resolving.org/urn:nbn:de:101:1-201305171104
ER  -