A stopping criterion for the conjugate gradient algorithm in the framework of anisotropic adaptive finite elements

We propose a simple stopping criterion for the conjugate gradient (CG) algorithm in the framework of anisotropic, adaptive finite elements for elliptic problems. The goal of the adaptive algorithm is to find a triangulation such that the estimated relative error is close to a given tolerance TOL. We propose to stop the CG algorithm whenever the residual vector has Euclidian norm less than a small fraction of the estimated error. This stopping criterion is based on a posteriori error estimates between the true solution u and the computed solution u(h)(n) (the superscript n stands for the CG iteration number, the subscript It for the typical mesh size) and on heuristics to relate the error between u(h) and u(h)(n) to the residual vector.


Published in:
Communications In Numerical Methods In Engineering, 25, 339-355
Year:
2009
Keywords:
Laboratories:




 Record created 2010-11-30, last modified 2018-01-28


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