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Uncertainty quantification for PDEs with anisotropic random diffusion

Harbrecht, Helmut and Peters, Michael and Schmidlin, Marc. (2016) Uncertainty quantification for PDEs with anisotropic random diffusion. Preprints Fachbereich Mathematik, 2016 (14).

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Official URL: https://edoc.unibas.ch/69978/

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Abstract

In this article, we consider elliptic diffusion problems with ananisotropic random diffusion coefficient. We model the notable direction in terms of a random vector field and derive regularity results for the solution's dependence on the random parameter. It turns out that the decay of the vector field's Karhunen-Loève expansion entirely determines this regularity. The obtained results allow for sophisticated quadrature methods, such as the quasi-Monte Carlo method or the anisotropic sparse grid quadrature, in order to approximate quantities of interest, like the solution's mean or the variance. Numerical examples in three spatial dimensions are provided to supplement the presented theory.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut and Peters, Michael and Schmidlin, Marc
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:22 Apr 2019 14:51
Deposited On:28 Mar 2019 09:51

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