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

This paper describes an enhanced error estimator for adaptive finite elemen t 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 co nventional recovery functional using the residual of the continuity equatio n for the constraint. The enhanced estimator, which we denote as LPRC, is t ested on unstructured second-order tetrahedral meshes using an analytical s olution to the three-dimensional incompressible Navier-Stokes equations. We report significant improvements in the effectiveness of the resulting erro r estimate, both for interior and boundary nodes, at virtually no additiona l computational cost. The LPRC estimator is particularly useful for flows i n which stresses at the boundary of the computational domain play an import ant role, such as in blood flow modeling. Although in this paper the LPRC e rror estimator is tested exclusively on the 10-noded tetrahedral Taylor-Hoo d element, we expect that when applied to incompressible flows, the LPRC es timator will perform more effectively than the LPR estimator when used with other types of elements as well. (C) 2001 Elsevier Science B.V. All rights reserved.