Goal-oriented a posteriori error estimates for transport problems

Some aspects of goal-oriented a posteriori error estimation are addressed in the context of steady convection–diffusion equations. The difference between the exact and approximate values of a linear target functional is expressed in terms of integrals that depend on the solutions to the primal and dual problems. Gradient averaging techniques are employed to separate the element residual and diffusive flux errors without introducing jump terms. The dual solution is computed numerically and interpolated using higher-order basis functions. A node-based approach to localization of global errors in the quantities of interest is pursued. A possible violation of Galerkin orthogonality is taken into account. Numerical experiments are performed for centered and upwind-biased approximations of a 1D boundary value problem.