A posteriori error estimators for the upstream weighting mixed methods for convection diffusion problems

摘要

In this paper, we design a posteriori error estimators for the mixed finite element approximation of the convection-diffusion problems with dominant convection which exhibit solutions with internal layers and boundary layers. A discontinuous upstream weighting scheme in association with the mixed method is used for the convection term. The a posteriori error estimator yields global upper and local lower bounds on the error measured in the L~2-norm. We present several numerical results to show the performance of the error estimator. We find that our estimator is not only reliable and efficient but also robust for various numerical examples.