Preconditioned GMRES methods for discretization equation of nonsymmetric and indefinite elliptic problem

Abstract

In this paper, a class of preconditioners for GMRES method are proposed for solving linear systems arising from discretization second-order nonsymmetric and indefinite elliptic problems by finite element method. The convergence of GMRES method is verified and the rate of convergence is shown. The generality of our result enables us to apply not only any known preconditioners designed for symmetric positive definite problems, but also many other preconditioners based on original operator to nonsymmetric and indefinite problems without losing optimality.