Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation
In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier--Stokes equations. In particular, we consider the a posteriori error analysis and...
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| Format: | Article |
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2005
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| Online Access: | https://eprints.nottingham.ac.uk/165/ |
| _version_ | 1848790353129242624 |
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| author | Hartmann, Ralf Houston, Paul |
| author_facet | Hartmann, Ralf Houston, Paul |
| author_sort | Hartmann, Ralf |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier--Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I a posteriori bounds are derived for the estimation of 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 dual 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 approach will be presented. |
| first_indexed | 2025-11-14T18:11:16Z |
| format | Article |
| id | nottingham-165 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:11:16Z |
| publishDate | 2005 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-1652020-05-04T20:30:33Z https://eprints.nottingham.ac.uk/165/ Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation Hartmann, Ralf Houston, Paul In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier--Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I a posteriori bounds are derived for the estimation of 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 dual 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 approach will be presented. 2005-07 Article PeerReviewed Hartmann, Ralf and Houston, Paul (2005) Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation. Discontinuous Galerkin methods a posteriori error estimation adaptivity compressible Navier-Stokes equations |
| spellingShingle | Discontinuous Galerkin methods a posteriori error estimation adaptivity compressible Navier-Stokes equations Hartmann, Ralf Houston, Paul Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation |
| title | Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation |
| title_full | Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation |
| title_fullStr | Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation |
| title_full_unstemmed | Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation |
| title_short | Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation |
| title_sort | symmetric interior penalty dg methods for the compressible navier-stokes equations ii: goal--oriented a posteriori error estimation |
| topic | Discontinuous Galerkin methods a posteriori error estimation adaptivity compressible Navier-Stokes equations |
| url | https://eprints.nottingham.ac.uk/165/ |