On higher-order-accuracy points in isoparametric finite element analysis and an application to error assessment

We consider the systematic calculation of higher-order-accuracy points in finite element analysis. The cases of varying material properties and distortion of elements are included. The results obtained are used to establish an error estimator that is element-based and applicable to varying material properties. Some example problems are solved and show the applicability of the error estimator. While one-dimensional problems are studied in detail, the extension to two- and three-dimensional analysis is indicated.