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.

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Author:Cornelia Kronsbein
URN (permanent link):urn:nbn:de:hbz:386-kluedo-33918
Advisor:Oleg Iliev
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2013/01/20
Year of Publication:2013
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute: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
Number of page:iii, 156
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 10.09.2012