TY - JOUR
T1 - Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation
AU - R. Hartmann & P. Houston
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 1
EP - 20
PY - 2006
DA - 2006/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/887.html
KW - discontinuous Galerkin methods, a posteriori error estimation, adaptivity, compressible Navier-Stokes equations.
AB - <p style="text-align: justify;">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.</p>