This paper derives upper and lower bounds for the -condition number of the stiffness matrix resulting from the finite element approximation of a linear, abstract model problem. Sharp estimates in terms of the meshsize are obtained. The theoretical results are applied to finite element approximations of elliptic PDE’s in variational and in mixed form, and to first-order PDE’s approximated using the Galerkin-Least Squares technique or by means of a non-standard Galerkin technique in . Numerical simulations are presented to illustrate the theoretical results.
@article{M2AN_2006__40_1_29_0,
author = {Ern, Alexandre and Guermond, Jean-Luc},
title = {Evaluation of the condition number in linear systems arising in finite element approximations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {40},
year = {2006},
pages = {29-48},
doi = {10.1051/m2an:2006006},
mrnumber = {2223503},
zbl = {pre05038391},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2006__40_1_29_0}
}
Ern, Alexandre; Guermond, Jean-Luc. Evaluation of the condition number in linear systems arising in finite element approximations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 40 (2006) pp. 29-48. doi : 10.1051/m2an:2006006. http://gdmltest.u-ga.fr/item/M2AN_2006__40_1_29_0/
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