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Volume 3, Issue 1
Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation

R. Hartmann & P. Houston

Int. J. Numer. Anal. Mod., 3 (2006), pp. 1-20.

Published online: 2006-03

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  • Abstract

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.

  • Keywords

discontinuous Galerkin methods, a posteriori error estimation, adaptivity, compressible Navier-Stokes equations.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-3-1, author = {R. Hartmann and P. Houston}, title = {Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {1}, pages = {1--20}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/887.html} }
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 -

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.

R. Hartmann and P. Houston. (2006). Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation. International Journal of Numerical Analysis and Modeling. 3 (1). 1-20. doi:
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