Adaptive h- p procedures for high accuracy finite element analysis of two-dimensional linear elastic problems

Abstract

Two adaptive procedures of the h- p version for a high accuracy finite element analysis of two-dimensional elastic problems are studied. These are based on a strategy of first using an h-version to predict a nearly optimal mesh up to a certain accuracy and then following up with a p-version to achieve a higher accuracy. The h-version, using linear triangular elements, is developed by coupling a code, ADMESH, with an error estimation in energy norm. Following the h-version, two alternative procedures of non-uniform p-refinements are then performed. In procedure I, p-refinements are made in one step by selectively adding hierarchical shape functions of order p = 2 and 3 based on the estimated error in energy norm. In procedure II, p-refinements are made in a step-by-step way by which, in the kth step of the p-refinements, hierarchical shape functions of order p = k + 1 are selectively introduced. In the first step of p-refinements of procedure II, hierarchical variables are selected by means of the estimated errors in energy norm, whereas in the later steps, they are selected with a guidance of an error estimate which evaluates the local average error of stresses. The performances of both procedures and the rate of convergence are studied in numerical examples. Numerical tests for the error estimates being used are also made. Obtained results indicate that both procedures can achieve a high accuracy (say, error below 5% measured in energy norm) in an exponential rate of convergence.