Enhanced error estimator for adaptive finite element analysis of 3D incompressible flow

Abstract

This paper describes an enhanced error estimator for adaptive finite element analysis of three-dimensional incompressible viscous flow. The estimator uses a modified form of the recovery functional employed in the well-known L 2 local patch recovery technique (LPR) originally proposed by Zienkiewicz and Zhu. The modified recovery functional is obtained by penalizing the conventional recovery functional using the residual of the continuity equation for the constraint. The enhanced estimator, which we denote as LPRC, is tested on unstructured second-order tetrahedral meshes using an analytical solution to the three-dimensional incompressible Navier–Stokes equations. We report significant improvements in the effectiveness of the resulting error estimate, both for interior and boundary nodes, at virtually no additional computational cost. The LPRC estimator is particularly useful for flows in which stresses at the boundary of the computational domain play an important role, such as in blood flow modeling. Although in this paper the LPRC error estimator is tested exclusively on the 10-noded tetrahedral Taylor–Hood element, we expect that when applied to incompressible flows, the LPRC estimator will perform more effectively than the LPR estimator when used with other types of elements as well.