Goal-oriented A Posteriori Error Estimates in Linearized Elasticity

Abstract

In this chapter, attention is focused on goal-oriented error estimation procedures that are based on generalized error measures because they are, in most cases, of greater interest to engineers than their energy norm counterparts. The error estimation procedures presented in the previous chapter for both Galerkin mesh-based and meshfree methods are extended in this chapter to provide an estimation of the generalized error measure. This error measure is typically related to the error of a given quantity of interest that naturally occurs in the design-specific computation of an engineering model within the computational V&V strategy. Examples of quantities of interest are local displacement or stress distributions and the fracture criterion in fracture mechanics problems, which is frequently a nonlinear quantity of interest that requires a linearization. To estimate the error of a given quantity of interest, a so-called dual problem needs to be solved in addition to the primal problem, which is, in this chapter, the conventional linearized elasticity problem. Moreover, a multi-space strategy is introduced that can use used to solve the dual problem on a different mesh or particle distribution and adds versatility to the goal-oriented error estimation procedures.