Iterative schemes for nonsymmetric and indefinite elliptic boundary value problems

Abstract

The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space H 1 ( Ω ) {H^1}(\Omega ) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right half of the complex plane. In fact, for symmetric indefinite problems, the iteration is reduced to a well-conditioned symmetric positive definite system which can be solved by conjugate gradient iteration. Applications of the general theory as well as numerical examples are given.