Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin finite element method

Bespalov, Alex and Praetorius, Dirk and Ruggeri, Michele (2021) Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin finite element method. SIAM-ASA Journal on Uncertainty Quantification, 9 (3). pp. 1184-1216. ISSN 2166-2525 (https://doi.org/10.1137/20M1342586)

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Abstract

The paper considers a class of parametric elliptic partial differential equations (PDEs), where the coefficients and the right-hand side function depend on infinitely many (uncertain) parameters. We introduce a two-level a posteriori estimator to control the energy error in multilevel stochastic Galerkin approximations for this class of PDE problems. We prove that the two-level estimator always provides a lower bound for the unknown approximation error, while the upper bound is equivalent to a saturation assumption. We propose and empirically compare three adaptive algorithms, where the structure of the estimator is exploited to perform spatial refinement as well as parametric enrichment. The paper also discusses implementation aspects of computing multilevel stochastic Galerkin approximations.

ORCID iDs

Bespalov, Alex, Praetorius, Dirk and Ruggeri, Michele ORCID logoORCID: https://orcid.org/0000-0001-6213-1602;
  • Item type:Article
    ID code:79759
    Dates:
    Date
    Event
    16 September 2021
    Published
    4 May 2021
    Accepted
    Subjects:Science > Mathematics
    Department:UNSPECIFIED
    Depositing user: Pure Administrator
    Date deposited:28 Feb 2022 17:04
    Last modified:11 Nov 2024 13:24
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/79759
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