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.
Mots clés : finite elements, condition number, partial differential equations, linear algebra
@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: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {29--48}, publisher = {EDP-Sciences}, volume = {40}, number = {1}, year = {2006}, doi = {10.1051/m2an:2006006}, mrnumber = {2223503}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2006006/} }
TY - JOUR AU - Ern, Alexandre AU - Guermond, Jean-Luc TI - Evaluation of the condition number in linear systems arising in finite element approximations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 29 EP - 48 VL - 40 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2006006/ DO - 10.1051/m2an:2006006 LA - en ID - M2AN_2006__40_1_29_0 ER -
%0 Journal Article %A Ern, Alexandre %A Guermond, Jean-Luc %T Evaluation of the condition number in linear systems arising in finite element approximations %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 29-48 %V 40 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2006006/ %R 10.1051/m2an:2006006 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 1, pp. 29-48. doi : 10.1051/m2an:2006006. http://www.numdam.org/articles/10.1051/m2an:2006006/
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