On selected efficient numerical methods for multiscale problems with stochastic coefficients
- Many real life problems have multiple spatial scales. In addition to the multiscale nature one has to take uncertainty into account. In this work we consider multiscale problems with stochastic coefficients. We combine multiscale methods, e.g., mixed multiscale finite elements or homogenization, which are used for deterministic problems with stochastic methods, such as multi-level Monte Carlo or polynomial chaos methods. The work is divided into three parts. In the first two parts we study homogenization with different stochastic methods. Therefore we consider elliptic stationary diffusion equations with stochastic coefficients. The last part is devoted to the study of mixed multiscale finite elements in combination with multi-level Monte Carlo methods. In the third part we consider multi-phase flow and transport equations.
Author: | Cornelia Kronsbein |
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URN: | urn:nbn:de:hbz:386-kluedo-33918 |
Advisor: | Oleg Iliev |
Document Type: | Doctoral Thesis |
Language of publication: | English |
Date of Publication (online): | 2013/01/20 |
Year of first Publication: | 2013 |
Publishing Institution: | Technische Universität Kaiserslautern |
Granting Institution: | Technische Universität Kaiserslautern |
Acceptance Date of the Thesis: | 2012/12/13 |
Date of the Publication (Server): | 2013/01/22 |
Tag: | Karhunen-Loève expansion; homogenization; mixed multiscale finite element methods; multi-level Monte Carlo; multi-phase flow; multiscale methods; stochastic coefficient |
GND Keyword: | Mehrskalenmodell; numerische Strömungssimulation; numerisches Verfahren |
Page Number: | iii, 156 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vom 10.09.2012 |