Chen, Wei; Křížek, Michal Lower bounds for the interpolation error for finite elements. (Chinese. English summary) Zbl 1212.41001 Math. Pract. Theory 39, No. 15, 159-164 (2009). Summary: We derive optimal lower bounds for the interpolation error of linear finite elements on quasiuniform partitions of an interval. A simple application based on superconvergence theory is given. In particular, we derive two-sided discretization error bounds by means of the interpolation error. MSC: 41A05 Interpolation in approximation theory 65D05 Numerical interpolation 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs Keywords:Lagrange finite element; Céa’s lemma; lower estimates PDF BibTeX XML Cite \textit{W. Chen} and \textit{M. Křížek}, Math. Pract. Theory 39, No. 15, 159--164 (2009; Zbl 1212.41001)