Error estimation and adaptivity for stochastic collocation finite elements. Part I: single-level approximation

Alex Bespalov, DJ Silvester, Feng Xu

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Abstract

A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by Guignard & Nobile in 2018 (SIAM J. Numer. Anal., 56, 3121-3143) to cover problems with a nonaffine parametric coefficient dependence. A suboptimal, but nonetheless reliable and convenient implementation of the strategy involves approximation of the decoupled PDE problems with a common finite element approximation space. Computational results obtained using such a single-level strategy are presented in this paper (part I). Results obtained using a potentially more efficient multilevel approximation strategy, where meshes are individually tailored, will be discussed in part II of this work. The codes used to generate the numerical results are available online.
Original languageEnglish
Pages (from-to)A3393-A3412
Number of pages20
JournalSIAM Journal on Scientific Computing
Volume44
Issue number5
Early online date20 Oct 2022
DOIs
Publication statusPublished - Oct 2022

Keywords

  • adaptivity
  • error estimation
  • PDEs with random data
  • finite element approximation
  • stochastic collocation

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