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

Abstract

Adjoint consistency - in addition to consistency - is the key requirement for discontinuous Galerkin discretizations to be of optimal order in L² as well as measured in terms of target functionals. We provide a general framework for analyzing adjoint consistency and introduce consistent modifications of target functionals. This framework is then used to derive an adjoint consistent discontinuous Galerkin discretization 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 <em>a posteriori</em> error estimation with respect to aerodynamical force coefficients on locally refined meshes.