A posteriori error estimate by element patch post-processing, adaptive analysis in energy and L2 norms

Abstract

This paper first presents a post-processing technique for obtaining a posteriori error estimators both in the energy norm and in the L 2 norm. For each element, an element patch, which represents the union of the considered element and its neighbours, is introduced. The post-processing for determining more accurate solutions is made by fitting a higher order polynomial expansion to the finite element solutions at superconvergent points in the patch by the least squares method. The element error estimate norms are calculated directly from the improved solutions. Another topic is the h-version adaptive finite element analysis for 2D linear elastic problems by coupling the error estimators with a mesh generator. T3 and T6 elements with the energy norm and a T6 element with the L 2 norm are used. Two examples, including a model for which exact solutions are available and a gravity dam under water pressure are presented. Numerical results show that the element patch post-processing provides asymptotically exact error estimates and the adaptive procedure produces finite element solutions with specified accuracy efficiently and economically.