Two-sided bounds of the discretization error for finite elements

0359285 - MÚ 2012 RIV FR eng J - Journal Article
Křížek, Michal - Roos, H.-G. - Chen, W.
Two-sided bounds of the discretization error for finite elements.
E S A I M: Mathematical Modelling and Numerical Analysis. Roč. 45, č. 5 (2011), s. 915-924. ISSN 0764-583X. E-ISSN 1290-3841
R&D Projects: GA AV ČR(CZ) IAA100190803
Institutional research plan: CEZ:AV0Z10190503
Keywords : Lagrange finite elements * Céa's lemma * superconvergence * lower error estimates
Subject RIV: BA - General Mathematics
Impact factor: 1.218, year: 2011
http://www.esaim-m2an.org/action/displayAbstract?fromPage=online&aid=8253942

We derive an optimal lower bound of the interpolation error for linear finite elements on a bounded two-dimensional domain. Using the supercloseness between the linear interpolant of the true solution of an elliptic problem and its finite element solution on uniform partitions, we further obtain two-sided a priori bounds of the discretization error by means of the interpolation error. Two-sided bounds for bilinear finite elements are given as well. Numerical tests illustrate our theoretical analysis.
Permanent Link: http://hdl.handle.net/11104/0197096