Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows
In this article we consider the construction of general isotropic and anisotropic adaptive mesh refinement strategies, as well as hp-mesh refinement techniques, for the numerical approximation of the compressible Euler and Navier-Stokes equations. To discretize the latter system of conservation laws...
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| Format: | Article |
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Institute for Scientific Computing and Information
2011
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| Online Access: | https://eprints.nottingham.ac.uk/1506/ |
| _version_ | 1848790620303261696 |
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| author | Giani, Stefano Houston, Paul |
| author_facet | Giani, Stefano Houston, Paul |
| author_sort | Giani, Stefano |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article we consider the construction of general isotropic and anisotropic adaptive mesh refinement strategies, as well as hp-mesh refinement techniques, for the numerical approximation of the compressible Euler and Navier-Stokes equations. To discretize the latter system of conservation laws,
we exploit the (adjoint consistent) symmetric version of the interior penalty discontinuous Galerkin finite element method. The a posteriori error indicators are derived based on employing the dual-weighted-residual approach in order to control the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain adjoint problem that must be numerically approximated. This general approach leads to the design of economical finite element meshes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed adaptive algorithms will be presented. |
| first_indexed | 2025-11-14T18:15:30Z |
| format | Article |
| id | nottingham-1506 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:15:30Z |
| publishDate | 2011 |
| publisher | Institute for Scientific Computing and Information |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-15062020-05-04T20:23:54Z https://eprints.nottingham.ac.uk/1506/ Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows Giani, Stefano Houston, Paul In this article we consider the construction of general isotropic and anisotropic adaptive mesh refinement strategies, as well as hp-mesh refinement techniques, for the numerical approximation of the compressible Euler and Navier-Stokes equations. To discretize the latter system of conservation laws, we exploit the (adjoint consistent) symmetric version of the interior penalty discontinuous Galerkin finite element method. The a posteriori error indicators are derived based on employing the dual-weighted-residual approach in order to control the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain adjoint problem that must be numerically approximated. This general approach leads to the design of economical finite element meshes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed adaptive algorithms will be presented. Institute for Scientific Computing and Information 2011 Article NonPeerReviewed Giani, Stefano and Houston, Paul (2011) Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. International Journal of Numerical Analysis and Modeling . ISSN 1705-5105 (Submitted) http://www.math.ualberta.ca/ijnam/AIMS.htm |
| spellingShingle | Giani, Stefano Houston, Paul Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows |
| title | Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows |
| title_full | Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows |
| title_fullStr | Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows |
| title_full_unstemmed | Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows |
| title_short | Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows |
| title_sort | anisotropic hp-adaptive discontinuous galerkin finite element methods for compressible fluid flows |
| url | https://eprints.nottingham.ac.uk/1506/ https://eprints.nottingham.ac.uk/1506/ |