Symmetric interior penalty DG methods for the compressible Navier-Stokes equations I: Method formulation
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 January 25, 2005
In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier-Stokes equations. For the discretization of the leading order terms, we propose employing the generalization of the symmetric version of the interior penalty method, originally developed for the numerical approximation of linear self-adjoint second-order elliptic partial differential equations. In order to solve the resulting system of nonlinear equations, we exploit a (damped) Newton GMRES algorithm. Numerical experiments demonstrating the practical performance of the proposed discontinuous Galerkin method with higher-order polynomials are 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)