The reliability of local error estimators for convection-diffusion equations (Q2713120)

The authors assess the reliability of a simple a posteriori error estimator for steady-state convection-diffusion equations in convection dominated cases. The estimator is computed by solving a local Poisson problem with Neumann boundary conditions. It gives global upper and local lower bounds on the error measured. However, the errors may be overestimated locally within boundary layers if these are not resolved by the mesh, that is, when the local mesh Péclet number is significantly greater than unity. The implications of this overestimation are discussed in a practical context.