A new error indicator based on stresses for three-dimensional elasticity

Abstract

As of now, most of the error indicators available for elastostatic problems are computed in terms of quantities that do not necessarily have the most relevant physical meaning from the point of view of a mechanical engineer. Furthermore, only few of them have been extended to three-dimensional problems where all the advantages of the boundary element method (BEM) over other numerical techniques are more evident. In this work, a new efficient and reliable error indicator for three-dimensional elastostatic problems is presented based on ideas previously developed by the authors for the two-dimensional case. This error indicator directly estimates the error in the numerical solution for the boundary stresses and exploits in its formulation the high accuracy in the nodal values for those quantities provided by Hermite-like higher order boundary elements. The basic idea behind the computation of the new error indicator is to compare, on an element-by-element basis, two different numerical solutions. The first solution is obtained from an analysis using Hermite-like elements. The second one is obtained by using some of the degrees of freedom of the Hermite-like elements to approximate the field variables inside the elements using conventional Lagrangian shape functions. In this sense, it is assumed that the bigger the difference among these two solutions, the bigger the error in the stresses computed with the Hermite-like elements. Since both solutions are obtained from just one analysis, the computational cost of the proposed error indicator is very low. Three numerical examples are presented to show that the results obtained using this new error indicator with an- h-adaptive strategy are satisfactory and very promising.