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#### The enriched Crouzeix-Raviart elements are equivalent to the Raviart-Thomas elements

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**Speaker(s)**Rui Ma (Peking University)**Date**From 2014-06-26 To 2014-06-26**Venue**Room 77201 at #78 courtyard, Beijing International Center for Mathematical Research

Speaker: Rui Ma (Peking University)

Time: Thu, 06/26/2014 - 16:30

Place: Room 77201 at #78 courtyard, Beijing International Center for Mathematical Research

Abstract: For both the Poisson model problem and the Stokes problem in any dimension, we prove 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 Laplace operator, this paper proves that the error of the enriched Crouzeix-Raviart element is equivalent to that of the Raviart-Thomas element up to higher order terms.