no. 1
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

This paper derives upper and lower bounds for the ℓ p -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 h 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 L 1 (Ω). Numerical simulations are presented to illustrate the theoretical results.

DOI : 10.1051/m2an:2006006
Classification : 65F35, 65N30
Keywords: finite elements, condition number, partial differential equations, linear algebra 
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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

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