The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem
- Journal Article
Rights / licenseIn Copyright - Non-Commercial Use Permitted
We present the formulation and the numerical analysis of the Brinkman problem derived in Allaire (Arch Rational Mech Anal 113(3): 209–259,1990. doi:10.1007/BF00375065, Arch Rational Mech Anal 113(3): 261–298, 1990. doi:10.1007/BF00375066) with a lognormal random permeability. Specifically, the permeability is assumed to be a lognormal random field taking values in the symmetric matrices of size d×d, where d denotes the spatial dimension of the physical domain D. We prove that the solutions admit bounded moments of any finite order with respect to the random input’s Gaussian measure. We present a Mixed Finite Element discretization in the physical domain D, which is uniformly stable with respect to the realization of the lognormal permeability field. Based on the error analysis of this mixed finite element method (MFEM), we develop a multi-level Monte Carlo (MLMC) discretization of the stochastic Brinkman problem and prove that the MLMC-MFEM allows the estimation of the statistical mean field with the same asymptotical accuracy versus work as the MFEM for a single instance of the stochastic Brinkman problem. The robustness of the MFEM implies in particular that the present analysis also covers the Darcy diffusion limit. Numerical experiments confirm the theoretical results. Show more
Journal / seriesNumerische Mathematik
Pages / Article No.
Organisational unit03435 - Schwab, Christoph / Schwab, Christoph
247277 - Automated Urban Parking and Driving (EC)
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Is new version of: https://doi.org/10.3929/ethz-a-010402591
NotesIt was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
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