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A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients

Dong, Zhaonan, Georgoulis, Emmanuil H., Levesley, Jeremy and Usta, Fuat 2018. A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients. Computers and Mathematics with Applications 76 (8) , pp. 1950-1965. 10.1016/j.camwa.2018.07.041

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Abstract

A new stochastic collocation finite element method is proposed for the numerical solution of elliptic boundary value problems (BVP) with random coefficients, assuming that the randomness is well-approximated by a finite number of random variables with given probability distributions. The proposed method consists of a finite element approximation in physical space, along with a stochastic collocation quadrature approach utilizing the recent Multilevel Sparse Kernel-Based Interpolation (MuSIK) technique (Georgoulis et al., 2013). MuSIK is based on a multilevel sparse grid-type algorithm with the basis functions consisting of directionally anisotropic Gaussian radial basis functions (kernels) placed at directionally-uniform grid-points. We prove that MuSIK is interpolatory at these nodes, and, therefore, can be naturally used to define a quadrature scheme. Numerical examples are also presented, assessing the performance of the new algorithm in the context of high-dimensional stochastic collocation finite element methods.

Item Type: Article
Date Type: Publication
Schools: Mathematics
Publisher: Elsevier
ISSN: 0898-1221
Date of First Compliant Deposit: 16 December 2019
Date of Acceptance: 29 July 2018
Last Modified: 17 Mar 2021 01:00
URI: http://orca.cf.ac.uk/id/eprint/127572

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