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# Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year

IMPACT FACTOR 2017: 0.658

CiteScore 2017: 1.05

SCImago Journal Rank (SJR) 2017: 1.291
Source Normalized Impact per Paper (SNIP) 2017: 0.893

Mathematical Citation Quotient (MCQ) 2017: 0.76

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1609-9389
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Volume 14, Issue 1

# Computational Survey on A Posteriori Error Estimators for the Crouzeix–Raviart Nonconforming Finite Element Method for the Stokes Problem

Carsten Carstensen
• Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany; and Department of Computational Science and Engineering, Yonsei University, 120-749 Seoul, Korea
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/ Christian Merdon
Published Online: 2013-09-05 | DOI: https://doi.org/10.1515/cmam-2013-0021

## Abstract.

This survey compares different strategies for guaranteed error control for the lowest-order nonconforming Crouzeix–Raviart finite element method for the Stokes equations. The upper error bound involves the minimal distance of the computed piecewise gradient ${D}_{NC}{u}_{CR}$ to the gradients of Sobolev functions with exact boundary conditions. Several improved suggestions for the cheap computation of such test functions compete in five benchmark examples. This paper provides numerical evidence that guaranteed error control of the nonconforming FEM is indeed possible for the Stokes equations with overall efficiency indices between 1 to 4 in the asymptotic range.

MSC: 65N30; 65N15

Published Online: 2013-09-05

Published in Print: 2014-01-01

Citation Information: Computational Methods in Applied Mathematics, Volume 14, Issue 1, Pages 35–54, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840,

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© 2014 by Walter de Gruyter Berlin/Boston.

## Citing Articles

[1]
Carsten Carstensen, Asha K. Dond, Neela Nataraj, and Amiya K. Pani
SIAM Journal on Numerical Analysis, 2018, Volume 56, Number 4, Page 2648
[2]
Carsten Carstensen and Sophie Puttkammer
Numerische Mathematik, 2018
[3]
Volker John, Alexander Linke, Christian Merdon, Michael Neilan, and Leo G. Rebholz
SIAM Review, 2017, Volume 59, Number 3, Page 492
[4]
P. Bringmann, C. Carstensen, and C. Merdon
Numerical Methods for Partial Differential Equations, 2016, Volume 32, Number 5, Page 1411
[5]