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Lower bounds for the interpolation error for finite elements. (Chinese. English summary) Zbl 1212.41001
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
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