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Even though substantial progress has been made in the numerical approximationof convection-dominated problems, its major challenges remain in the scope ofcurrent research. In particular, parameter robust a posteriori error estimatesfor quantities of physical interest and adaptive mesh refinement strategieswith proved convergence are still missing. Here, we study numerically thepotential of the Dual Weighted Residual (DWR) approach applied to stabilizedfinite element methods to further enhance the quality of approximations. Theimpact of a strict application of the DWR methodology is particularly focusedrather than the reduction of computational costs for solving the dual problemby interpolation or localization.

Dual weighted residual based error control for nonstationary convection-dominated equations: potential or ballast?