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• W2963864251 abstract "We consider elliptic diffusion problems with a random anisotropic diffusion coefficient, where, in a notable direction given by a random vector field, the diffusion strength differs from the diffusion strength perpendicular to this notable direction. The Karhunen–Loève expansion then yields a parametrisation of the random vector field and, therefore, also of the solution of the elliptic diffusion problem. We show that, given regularity of the elliptic diffusion problem, the decay of the Karhunen–Loève expansion entirely determines the regularity of the solution’s dependence on the random parameter, also when considering this higher spatial regularity. This result then implies that multilevel quadrature methods may be used to lessen the computation complexity when approximating quantities of interest, like the solution’s mean or its second moment, while still yielding the expected rates of convergence. Numerical examples in three spatial dimensions are provided to validate the presented theory." @default.
• W2963864251 created "2019-07-30" @default.
• W2963864251 creator A5005562022 @default.
• W2963864251 creator A5063917682 @default.
• W2963864251 date "2019-05-27" @default.
• W2963864251 modified "2023-10-14" @default.
• W2963864251 title "Multilevel methods for uncertainty quantification of elliptic PDEs with random anisotropic diffusion" @default.
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• W2963864251 doi "https://doi.org/10.1007/s40072-019-00142-w" @default.
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