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The Enriched Crouzeix---Raviart Elements are Equivalent to the Raviart---Thomas Elements

Authors:

Rui MaAuthors Info & Claims

Journal of Scientific Computing, Volume 63, Issue 2

Pages 410 - 425

https://doi.org/10.1007/s10915-014-9899-9

Published: 01 May 2015 Publication History

Abstract

For both the Poisson model problem and the Stokes problem in any dimension, this paper proves that the enriched Crouzeix---Raviart elements are actually identical to the first order Raviart---Thomas elements in the sense that they produce the same discrete stresses. This result improves the previous result in literature which, for two dimensions, states that the piecewise constant projection of the stress by the first order Raviart---Thomas element is equal to that by the Crouzeix---Raviart element. For the eigenvalue problem of the Laplace operator, this paper proves that the error of the enriched Crouzeix---Raviart element is equivalent to that of the first order Raviart---Thomas element up to higher order terms.

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Cited By

Dell'Accio FGuessab ANudo F(2024)New quadratic and cubic polynomial enrichments of the Crouzeix–Raviart finite elementComputers & Mathematics with Applications10.1016/j.camwa.2024.06.019170:C(204-212)Online publication date: 15-Sep-2024
https://dl.acm.org/doi/10.1016/j.camwa.2024.06.019
Nakano TLiu X(2023)Guaranteed local error estimation for finite element solutions of boundary value problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2023.115061425:COnline publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1016/j.cam.2023.115061
Hu JMa LMa R(2021)Optimal superconvergence analysis for the Crouzeix-Raviart and the Morley elementsAdvances in Computational Mathematics10.1007/s10444-021-09874-747:4Online publication date: 29-Jun-2021
https://dl.acm.org/doi/10.1007/s10444-021-09874-7

The Enriched Crouzeix---Raviart Elements are Equivalent to the Raviart---Thomas Elements
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations

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cover image Journal of Scientific Computing

Journal of Scientific Computing Volume 63, Issue 2

May 2015

325 pages

ISSN:0885-7474

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Copyright © Copyright © 2015 Springer Science+Business Media New York.

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Plenum Press

United States

Publication History

Published: 01 May 2015

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Cited By

Dell'Accio FGuessab ANudo F(2024)New quadratic and cubic polynomial enrichments of the Crouzeix–Raviart finite elementComputers & Mathematics with Applications10.1016/j.camwa.2024.06.019170:C(204-212)Online publication date: 15-Sep-2024
https://dl.acm.org/doi/10.1016/j.camwa.2024.06.019
Nakano TLiu X(2023)Guaranteed local error estimation for finite element solutions of boundary value problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2023.115061425:COnline publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1016/j.cam.2023.115061
Hu JMa LMa R(2021)Optimal superconvergence analysis for the Crouzeix-Raviart and the Morley elementsAdvances in Computational Mathematics10.1007/s10444-021-09874-747:4Online publication date: 29-Jun-2021
https://dl.acm.org/doi/10.1007/s10444-021-09874-7

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