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

Mark Ainsworth; Alejandro Allendes; Gabriel R. Barrenechea; Richard Rankin

doi:10.1093/imanum/drr006

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

Mark Ainsworth, Alejandro Allendes, Gabriel R. Barrenechea, Richard Rankin

Research output: Journal Publication › Article › peer-review

6 Citations (Scopus)

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.

Original language	English
Pages (from-to)	417-447
Number of pages	31
Journal	IMA Journal of Numerical Analysis
Volume	32
Issue number	2
DOIs	https://doi.org/10.1093/imanum/drr006
Publication status	Published - Apr 2012
Externally published	Yes

Keywords

A posteriori error estimation
Fortin-Soulie element
Nonconforming finite element

ASJC Scopus subject areas

General Mathematics
Computational Mathematics
Applied Mathematics

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10.1093/imanum/drr006

Cite this

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title = "Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem",

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.",

keywords = "A posteriori error estimation, Fortin-Soulie element, Nonconforming finite element",

author = "Mark Ainsworth and Alejandro Allendes and Barrenechea, {Gabriel R.} and Richard Rankin",

note = "Funding Information: The Engineering and Physical Sciences Research Council of Great Britain under the Numerical Algorithms and Intelligent Software for the evolving HPC platform (EP/G036136/1 to M.A. and R.R.); The Faculty of Science of Strathclyde University and Comisi{\'o}n Nacional de Investigaci{\'o}n Cient{\'i}fica y Tecnol{\'o}gica—CONICYT (Chile) through a research studentship (to A.A.).",

year = "2012",

month = apr,

doi = "10.1093/imanum/drr006",

language = "English",

volume = "32",

pages = "417--447",

journal = "IMA Journal of Numerical Analysis",

issn = "0272-4979",

publisher = "Oxford University Press",

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T1 - Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem

AU - Ainsworth, Mark

AU - Allendes, Alejandro

AU - Barrenechea, Gabriel R.

AU - Rankin, Richard

N1 - Funding Information: The Engineering and Physical Sciences Research Council of Great Britain under the Numerical Algorithms and Intelligent Software for the evolving HPC platform (EP/G036136/1 to M.A. and R.R.); The Faculty of Science of Strathclyde University and Comisión Nacional de Investigación Científica y Tecnológica—CONICYT (Chile) through a research studentship (to A.A.).

PY - 2012/4

Y1 - 2012/4

N2 - 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.

AB - 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.

KW - A posteriori error estimation

KW - Fortin-Soulie element

KW - Nonconforming finite element

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U2 - 10.1093/imanum/drr006

DO - 10.1093/imanum/drr006

M3 - Article

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EP - 447

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JF - IMA Journal of Numerical Analysis

IS - 2

ER -

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

Abstract

Keywords

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