Naslov
Ritz value estimates and applications in Mathematical Physics

Autori
Grubišić, Luka

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
Fachbereich Mathematik

Mjesto
Hagen

Datum
03.05

Godina
2005

Stranica
174

Mentor
Veselić, Krešimir

Ključne riječi
Eigenvalue ; Eigenvector ; Elliptic-Operator ; Sylvester-Equation

Sažetak
This thesis is about presenting a (new) general theory on Ritz value spectral approximations for elliptic self-adjoint operators. These results extend the known Davis--Kahan estimates to operators defined as quadratic forms. As a first application, we have considered the problem of computing rigorous spectral estimates for problems of the large coupling limit (for both eigenvalues and spectral families). In this context two problem classes have been identified: the regular case which encompasses problems from the elasticity theory (Arch/Curved Rod, Lame/Stokes) and the second class of problems (Schroedinger/Dirichlet, Helmholtz/Dirichlet) which does not satisfy the new regularity requirement. As a second class of problems we have studied the spectral finite element approximations for operators which are not H2 regular.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA