Ralf Hartmann
Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation
Hartmann, Ralf; Houston, Paul
Abstract
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.
Citation
Hartmann, R., & Houston, P. (2005). Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation
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 | Discontinuous Galerkin methods, a posteriori error estimation, adaptivity, compressible Navier-Stokes equations |
Public URL | https://nottingham-repository.worktribe.com/output/1019944 |
Files
compns_part2.pdf
(4.9 Mb)
PDF
You might also like
Linearization of the Travel Time Functional in Porous Media Flows
(2022)
Journal Article
Gibbs phenomena for Lq-best approximation in finite element spaces
(2022)
Journal Article
Downloadable Citations
About Repository@Nottingham
Administrator e-mail: digital-library-support@nottingham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search