Stopping criteria for iterations in finite element methods (Q1769085)

This paper is devoted to stopping criteria for iterative solution methods for linear finite element methods for nonsymmetric positive-definite problems. It is a generalization of \textit{M. Arioli}'s previous results [Numer. Math. 97, No. 1, 1--24 (2004; Zbl 1048.65029)]. The authors prove 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 and then use Krylov solvers as alternative ways of calculating or estimating this quantity. Some numerical experiments are presented to show the validity of the criteria.