Symmetric interior penalty DG methods for the compressible Navier-Stokes equations II: Goal-oriented a posteriori error estimation
Ralf Hartmann 1, Paul Houston 21 Institute of Aerodynamics and Flow Technology, German Aerospace Center, Lilienthalplatz 7, 38108 Braunschweig, Germany
2 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
Received by the editors March 20, 2005.
In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier-Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I aposteriori bounds are derived for the estimation of the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated. This general approach leads to the design of economical finite element me shes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed approach will be presented.
AMS subject classifications: 65N15, 65N30
Key words: discontinuous Galerkin methods; a posteriori error estimation; adaptivity; compressible Navier-Stokes equations
Email: Ralf.Hartmann@dlr.de (R. Hartmann), Paul.Houston@nottingham.ac.uk (P. Houston)