Error estimates of triangular finite elements under a weak angle condition

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.