Computable error bounds for nonconfirming Fortin-Soulie finite element approximation of the Stokes problem

Ainsworth, Mark and Allendes Flores, Alejandro Ignacio and Barrenechea, Gabriel and Rankin, Richard Andrew Robert (2012) Computable error bounds for nonconfirming Fortin-Soulie finite element approximation of the Stokes problem. IMA Journal of Numerical Analysis, 32 (2). pp. 414-447. ISSN 0272-4979 (https://doi.org/10.1093/imanum/drr006)

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Abstract

We propose computable a posteriori error estimates for a second order nonconforming finite element approximation of the Stokes problem. The estimator is completely free of unknown constants and gives a guaranteed numerical upper bound on the error, in terms of a lower bound for the inf-sup constant of the underlying continuous problem. The estimator is also shown to provide a lower bound on the error up to a constant and higher order data oscillation terms. Numerical results are presented illustrating the theory and the performance of the estimator.

ORCID iDs

Ainsworth, Mark, Allendes Flores, Alejandro Ignacio, Barrenechea, Gabriel ORCID logoORCID: https://orcid.org/0000-0003-4490-678X and Rankin, Richard Andrew Robert;
  • Item type:Article
    ID code:39488
    Dates:
    Date
    Event
    2012
    Published
    Keywords:a posteriori error estimation, Fortin-Soulie element , nonconforming finite element, Mathematics, Computational Mathematics, Applied Mathematics, Mathematics(all)
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:02 May 2012 15:53
    Last modified:25 Mar 2023 04:14
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/39488
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