Error estimates of triangular finite elements under a weak angle condition

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.