Superconvergent patch recovery techniques – some further tests

Abstract

SUMMARYA modification has been introduced to the new superconvergent patch derivative recovery technique recently developed (Zienkiewicz and Zhu, 1991). By use of a locally normalized co-ordinate system, the application of this technique can now be applied to higher-order finite-element shape functions. Numerical studies are carried out for up to 6th-order elements in one dimension and for up to quartic elements in two dimensions, and superconvergent results are obtained for all examples tested.

Incremental‐secant modulus iteration scheme and stress recovery for simulating cracking process in quasi‐brittle materials using XFEM

“…This was overcome by using a larger domain of influence (DOI) including more sampling points in Xiao and Karihaloo [25]. An alternative way is to introduce locally normalized co-ordinates running from −1 to +1 as suggested by Zienkiewicz et al [26]. This can be done as follows.…”

“…Techniques for handling non-homogeneous tractions on the boundary will be discussed. Furthermore, the normalization of local co-ordinates suggested by Zienkiewicz et al [26] will be employed to eliminate the possible ill-conditioning of MLS. The influence of different weight functions on the recovered stresses of SAR will also be studied.…”

Validation of A-Posteriori Error Estimators by Numerical Approach

“…Error estimators based on recovery methods are given in [33][34][35][36][37][38][39][40][41][42][43][44]. Here we focus on the superconvergent patch-recovery technique [40][41][42][43][44].…”

“…Here we focus on the superconvergent patch-recovery technique [40][41][42][43][44]. The element error-indicators for elements of any degree p are …”

A Study on the Pollution Error in r-h Methods Using Singular Shape Functions

“…The pollution error estimator makes up for the weak points of the local error estimators. It was demonstrated that the conventional ZienkiewiczZhu error estimator [5,6,7,8] was insufficient and should include a pollution error indicator [1,4]. The pollution-adaptive feedback algorithm employs both local error indicators and pollution error indicators to refine the mesh outside a larger patch, which includes a patch and one to two surrounding mesh layers [2,3].…”