Local a Posteriori Error Estimator Based on the Hypercircle Method

The error of the finite element solution of linear elliptic problems can be estimated a posteriori by the classical hypercircle method. This method gives accurate and guaranteed upper bound of the error measured in the energy norm. The disadvantage is that a global dual problem has to be solved, which is quite time-consuming. Combining the hypercircle method with the equilibrated residual method, we obtain locally computable guaranteed upper bound. The computer implementation of this a posteriori error estimator is also discussed.