Neumann-Type A Posteriori Error Estimation For Steady Convection-Diffusion Equation

ABSTRACT We consider a steady linear convection diffusion equation in 2D present the standard Galerkin GK approximation and the Streamline-Diffusion Finite Element Method SDFEM and give an analysis of a posteriori error estimator based on solving a local Neumann problem. The estimator gives global upper and local lower bounds on the error measured in the H1 semi-norm. Our numerical results from GK and SD approximations show that the global effectivity indices deteriorate in rates O2612310Pe2612311K and O2687302612310Pe2612311K as 2612310Pe2612311K268594268734 respectively i.e. the estimator is over-estimated the error locally within a boundary layer which is not resolved by uniform grid refinement.