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Evaluation of the condition number in linear systems arising in finite element approximations

Alexandre Ern, Jean-Luc Guermond (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper derives upper and lower bounds for the 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 L1(Ω). Numerical...

Explicit conjugate gradient method with preconditioning

Jitka Křížková, Petr Vaněk (1994)

Applications of Mathematics

An algorithm of the preconditioned conjugate gradient method in which the solution of an auxiliary system is replaced with multiplication by the matrix M = I - ω A for suitably chosen ω is presented.

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