Two-sided bounds of the discretization error for finite elements
Institute of Mathematics, Academy of Sciences,
Žitná 25, 115 67 Prague 1, Czech Republic. email@example.com
2 Institute of Numerical Mathematics, Technical University Dresden, Zellescher Weg 12–14, 01069 Dresden, Germany. firstname.lastname@example.org
3 School of Economics, Shandong University, 27 Shanda Nanlu, Jinan 250 100, P.R. China. email@example.com
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.
Mathematics Subject Classification: 65N30
Key words: Lagrange finite elements / Céa's lemma / superconvergence / lower error estimates.
© EDP Sciences, SMAI, 2011