On local error estimators for non-self-adjoint boundary value problems

The study focuses on an adaptive finite element method for the stationary c onvection-diffusion problem with dominant convection. A short review of the standard and stabilised finite element method will be given. The adaptivit y scheme is based on an a posteriori error estimator for local quantities. In this error estimation strategy for a non-self-adjoint boundary value pro blem we introduce duality techniques or in engineering words we use an infl uence function related to the reciprocal theorem of BETTI & MAXWELL to esti mate the local errors. With this type of error estimator, the pollution eff ect in the domain Omega caused by shock fronts or boundary layers could be captured.