A posteriori error estimators for the upstream weighting mixed methods for convection diffusion problems
In this paper, we design a posteriori error estimators for the mixed finite element approximation of the convectiondiffusion 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 L2-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.
65k10 65m12 65m60