MULTILEVEL PRECONDITIONING FOR PERTURBED FINITE-ELEMENT MATRICES

Multilevel preconditioning methods for finite element matrices for the approximation of second-order elliptic problems are considered. Using perturbations of the local finite element matrices by zero-order term s it is shown that one can control the smallest eigenvalues. In this w ay in a multilevel method one can reach a final coarse mesh, where the remaining problem to be solved has a condition number independent of the total degrees of freedom, much earlier than if no perturbations we re used. Hence, there is no need in a method of optimal computational complexity to carry out the recursion in the multilevel method to a co arse mesh with a fixed number of degrees of freedom.