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.
Keywords: conjugate gradient algorithm ; stopping criterion ; a posteriori error estimates ; anisotropic adaptive finite elements ; Posteriori Error Estimator ; High-Aspect-Ratio ; Mesh Adaptation ; Elliptic Problems ; Computations
Record created on 2010-11-30, modified on 2016-08-09