a1 CERMICS, École nationale des ponts et chaussées, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France. firstname.lastname@example.org
a2 Dept. Math, Texas A&M, College Station, TX 77843-3368, USA and LIMSI (CNRS-UPR 3152), BP 133, 91403, Orsay, France. email@example.com
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 L 1(Ω). Numerical simulations are presented to illustrate the theoretical results.
(Received March 7 2005)
(Revised July 6 2005)
(Online publication February 23 2006)
Mathematics Subject Classification: