Error estimates of triangular finite elements under a weak angle condition

Authors:
Shipeng Mao;Zhongci Shi
Affiliations:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Science, Chinese Academy of Science, PO Box 2719, Beijing, 100190, PR China;LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Science, Chinese Academy of Science, PO Box 2719, Beijing, 100190, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this note, by analyzing the interpolation operator of Girault and Raviart given in [V. Girault, P.A. Raviart, Finite element methods for Navier-Stokes equations, Theory and algorithms, in: Springer Series in Computational Mathematics, Springer-Verlag, Berlin,1986] over triangular meshes, we prove optimal interpolation error estimates for Lagrange triangular finite elements of arbitrary order under the maximal angle condition in a unified and simple way. The key estimate is only an application of the Bramble-Hilbert lemma.