A robust a-posteriori error estimator for discontinuous Galerkin methods for convection–diffusion equations

A robust a-posteriori error estimator for interior penalty discontinuous Galerkin discretizations of a stationary convection–diffusion equation is derived. The estimator yields global upper and lower bounds of the error measured in terms of the energy norm and a semi-norm associated with the convective term in the equation. The ratio of the upper and lower bounds is independent of the magnitude of the Péclet number of the problem, and hence the estimator is fully robust for convection-dominated problems. Numerical examples are presented that illustrate the robustness and practical performance of the proposed error estimator in an adaptive refinement strategy.