Volume 40, Number 1, January-February 2006
|Page(s)||29 - 48|
|Published online||23 February 2006|
Evaluation of the condition number in linear systems arising in finite element approximations
CERMICS, École nationale des ponts et chaussées,
Champs sur Marne, 77455 Marne la Vallée Cedex 2, France. firstname.lastname@example.org
2 Dept. Math, Texas A&M, College Station, TX 77843-3368, USA and LIMSI (CNRS-UPR 3152), BP 133, 91403, Orsay, France. email@example.com
Revised: 6 July 2005
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 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 L1(Ω). Numerical simulations are presented to illustrate the theoretical results.
Mathematics Subject Classification: 65F35 / 65N30
Key words: Finite elements / condition number / partial differential equations / linear algebra.
© EDP Sciences, SMAI, 2006
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