Evaluation of the Condition Number in Linear Systems Arising in Finite Element Approximations

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(Ω). Numerical simulations are presented to illustrate the theoretical results. Mathematics Subject Classification. 65F35, 65N30. Received: March 7, 2005. Revised: July 6, 2005.