Stopping criteria for iterations in finite element methods

Authors:
M. Arioli;D. Loghin;A. J. Wathen
Affiliations:
Rutherford Appleton Laboratory, Atlas Centre, OX11 0QX, Oxon, UK;CERFACS, Atlas Centre, 42 ave G. Coriolis, 31057, Toulouse, France;Oxford University Computing Laboratory, Atlas Centre, Parks Road, OX1 3QD, Oxford, UK
Venue:
Numerische Mathematik
Year:
2005

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Abstract

This work extends the results of Arioli [1], [2] on stopping criteria for iterative solution methods for linear 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 use Krylov solvers to provide alternative ways of calculating or estimating this quantity and present numerical experiments which validate our criteria.