Stopping criteria for iterations in finite element methods

This work extends the results of Arioli [1], [2] on stopping criteria for iterative solution methods for finite element problems to the case of nonsymmetric positive-definite problems. We show that the residual measured in the norm induced by the symmetric part of the inverse of the system matrix is relevant to convergence in a finite element context. We then provide alternative ways of calculating or estimating this quantity and present numerical experiments which validate our criteria.