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Symmetric Interior Penalty DG Methods for the Compressible
Navier-Stokes Equations I: Method Formulation

Hartmann, Ralf; Houston, Paul


Ralf Hartmann

Professor of Computational and Applied Maths


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.


Navier-Stokes Equations I: Method Formulation

Journal Article Type Article
Publication Date Jul 1, 2005
Deposit Date Aug 5, 2005
Publicly Available Date Oct 9, 2007
Peer Reviewed Peer Reviewed
Keywords Finite element methods, discontinuous Galerkin methods,
compressible Navier-Stokes equations
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