Application of Zienkiewicz—Zhu’s error estimate with superconvergent patch recovery to hierarchical p-refinement
نویسندگان
چکیده
The Zienkiewicz—Zhu error estimate is slightly modified for the hierarchical p-refinement, and is then applied to three plane elastostatic problems to demonstrate its effectiveness. In each case, the error decreases rapidly with an increase in the number of degrees of freedom. Thus Zienkiewicz—Zhu’s error estimate can be used in the hp-refinement of finite element meshes. ( 1999 Elsevier Science B.V. All rights reserved.
منابع مشابه
Analysis of the Superconvergent Patch Recovery Technique and a Posteriori Error Estimator in the Finite Element Method (i)
SUMMARY This is the rst in a series of two papers in which the patch recovery technique proposed by Zienkiewicz and Zhu is analyzed. In this work, it is proved that the recovered derivative by the least squares tting is superconvergent for the two point boundary value problems. Further the a posteriori error estimator based on the recovery technique is show to be asymptotically exact. This conn...
متن کاملAnalysis of the Superconvergent Patch Recovery Technique and a Posteriori Error Estimator in the Finite Element Method (ii)
SUMMARY This is the second in a series of two papers in which the patch recovery technique proposed by Zienkiewicz and Zhu 1]-3] is analyzed. In the rst paper 4], we have shown that the recovered derivative by the least squares tting is superconvergent for the two point boundary value problems. In the present work, we consider the two dimensional case in which the tensor product elements are us...
متن کاملMathematical Analysis of Zienkiewicz - Zhu ' sDerivative Patch Recovery
Zienkiewicz-Zhu's derivative patch recovery technique is analyzed for general quadri-lateral nite elements. Under certain regular conditions on the meshes, the arithmetic mean of the absolute error of the recovered gradient at the nodal points is superconver-gent for the second-order elliptic operators. For rectangular meshes and the Laplacian, the recovered gradient is superconvergent in the m...
متن کاملAdaptive Mesh Refinement for High-Resolution Finite Element Schemes
New a posteriori error indicators based on edgewise slope-limiting are presented. The L2-norm is employed to measure the error of the solution gradient in both global and element sense. A second order Newton-Cotes formula is utilized in order to decompose the local gradient error from a P1-finite element solution into a sum of edge contributions. The gradient values at edge midpoints are interp...
متن کاملA New Finite Element Gradient Recovery Method: Superconvergence Property
This is the first in a series of papers where a new gradient recovery method is introduced and analyzed. It is proved that the method is superconvergent for translation invariant finite element spaces of any order. The method maintains the simplicity, efficiency, and superconvergence properties of the Zienkiewicz-Zhu patch recovery method. In addition, under uniform triangular meshes, the metho...
متن کامل