Goal-oriented a posteriori error estimates in nearly incompressible linear elasticity

Abstract

In this article, we consider linear elastic problems, where Poisson’s ratio is close to 0.5 leading to nearly incompressible material behavior. The use of standard linear or d-linear finite elements involves locking phenomena in the considered problem type. One way to overcome this difficulties is given by selective reduced integration. However, the discrete problem differs from the continuous one using this approach. This fact has especially to be taken into account, when deriving a posteriori error estimates. Here, we present goal-oriented estimates based on the dual weighted residual method using only the primal residual due to the linear problem considered. The major challenge is given by the construction of an appropriate numerical approximation of the error identity. Numerical results substantiate the accuracy of the presented estimator and the efficiency of the adaptive method based on it.