Adaptive Discontinuous Galerkin Finite Element Methods with Interior Penalty for the Compressible Navier-Stokes Equations

Abstract

In this article we consider 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 derive a posteriori error estimates for the estimation of the error, measured in terms of general target quantities of the solution like e.g. the drag and lift coefficients. These error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual (adjoint) problem that must be numerically approximated. An adaptive mesh design based on the local error indicators leads to finite element meshes specifically tailored to the efficient computation of the target quantities. Numerical experiments for a laminar flow around a NACA0012 airfoil are included.