A Posteriori Error Estimators for the NonconformingP 1 { Finite Element Discretization

In this paper we focus on adaptive methods for discretizing convection{diiusion equations by means of the nonconforming P 1 {{nite element. Local lower estimates for residual based a posteriori error estimators in a discrete H 1 {norm and in the L 2 {norm are proven. Moreover, a residual based a posteriori error estimator in the L 2 {norm is derived. The behaviour of local error estimators is illustrated by numerical examples. Finally, we compare the global error estimate with the real error numerically and describe a way of approximating the size of a stability constant which is essential for the reliability of the error estimate.