| Issue |
ESAIM: M2AN
Volume 40, Number 1, January-February 2006
|
|
|---|---|---|
| Page(s) | 29 - 48 | |
| DOI | https://doi.org/10.1051/m2an:2006006 | |
| Published online | 23 February 2006 | |
Evaluation of the condition number in linear systems arising in finite element approximations
1
CERMICS, École nationale des ponts et chaussées,
Champs sur Marne, 77455 Marne la Vallée Cedex 2, France. ern@cermics.enpc.fr
2
Dept. Math, Texas A&M, College Station, TX
77843-3368, USA and
LIMSI (CNRS-UPR 3152), BP 133, 91403, Orsay, France. guermond@math.tamu.edu
Received:
7
March
2005
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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