Error estimation and adjoint based refinement for an adjoint consistent DG discretisation of the compressible Euler equations

Adjoint consistency – in addition to consistency – is the key requirement for discontinuous Galerkin discretisations to be of optimal order in L as well as measured in terms of target functionals. We provide a general framework for analysing adjoint consistency and introduce consistent modifications of target functionals. This framework is then used to derive an adjoint consistent discontinuous Galerkin discretisation of the compressible Euler equations. We demonstrate the effect of adjoint consistency on the accuracy of the flow solution, the smoothness of the discrete adjoint solution and the a posteriori error estimation with respect to aerodynamical force coefficients on locally refined meshes.