TY - JOUR T1 - Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal-Oriented a Posteriori Error Estimation JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 141 EP - 162 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/894.html KW - discontinuous Galerkin methods, a posteriori error estimation, adaptivity, compressible Navier-Stokes equations. AB -

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 a posteriori 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 meshes 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.