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Stopping criteria for iterations in finite element methods. (English) Zbl 1069.65124
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 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.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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