Abstract
In this paper, we present a subdomain residual method which gives a posteriori estimates of the errors in finite element solutions of viscoelastic fluid flows. We employ a coupled approach in which the estimated errors in both velocity and extra stress are computed simultaneously by solving a series of local problems. The subdomains on which the local problems are posed consist of patches of elements. A given parameter which is independent of the element size is employed to determine the size of the subdomains to ensure that the error estimate improves as the element size is reduced. The error estimator is applied to finite element solutions of Newtonian and non-Newtonian fluid flows past a cylindrical tube in a duct. The contour plots of the components of the estimated errors in velocity and extra stress are presented. These errors are compared with reference errors.
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