University of Leicester
Browse
A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients.pdf (555.05 kB)

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

Download (555.05 kB)
journal contribution
posted on 2018-09-07, 14:42 authored by Zhaonan Dong, Emmanuil H. Georgoulis, Jeremy Levesley, Fuat Usta
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.

History

Citation

Computers and Mathematics with Applications, 2018

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • AM (Accepted Manuscript)

Published in

Computers and Mathematics with Applications

Publisher

Elsevier

issn

0898-1221

Acceptance date

2018-07-29

Copyright date

2018

Available date

2019-08-23

Publisher version

https://www.sciencedirect.com/science/article/pii/S0898122118304127?via=ihub

Notes

The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.

Language

en

Usage metrics

    University of Leicester Publications

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC