A posteriori estimation and adaptive control of the error in the quantity of interest. Part I: A posteriori estimation of the error in the von Mises stress and the stress intensity factor

In this paper we address the problem of a posteriori estimation of the erro r in an engineering quantity of interest which is computed from a finite el ement solution. As an example we consider the plane elasticity problem with the von Mises stress and the stress intensity factor, as the quantities of interest. The estimates of the error in the von Mises stress at a point ar e obtained by partitioning the error into two components with respect to th e element which includes the point, the local and the pollution errors; and by constructing separate estimates for each component. The estimates of th e error in the stress intensity factors are constructed by employing an ext raction method. We demonstrate that our approach gives accurate estimates f or rather coarse meshes and elements of various degrees. In Part II we will address the problem of the adaptive control of the error in the quantity o f interest (the goal of the computation), and the construction of goal-adap tive meshes for one or multiple goals. (C) 2000 Published by Elsevier Scien ce S.A. All rights reserved.