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

Authors:
R. Hartmann
Affiliations:
Institute of Aerodynamics and Flow Technology, German Aerospace Center (/DLR)/, Braunschweig, Germany/ Institute of Scientific Computing, TU Braunschweig, Germany
Venue:
International Journal of Computing Science and Mathematics
Year:
2007

Citing 5
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Abstract

Adjoint consistency in addition to consistency is the key requirement for discontinuous Galerkin discretisations to be of optimal order in L2 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.