Hartmann, Ralf and Houston, Paul (2006) Symmetric Interior Penalty DG Methods for the Compressible Navier--Stokes Equations II: Goal--Oriented A Posteriori Error Estimation. International Journal of Numerical Analysis & Modeling, 3 (2), pp. 141-162.
![]()
|
PDF
5MB |
Official URL: http://www.math.ualberta.ca/ijnam/Volume-3-2006/No-2-06/2006-02-02.pdf
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.
Item URL in elib: | https://elib.dlr.de/44202/ | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Document Type: | Article | ||||||||||||
Title: | Symmetric Interior Penalty DG Methods for the Compressible Navier--Stokes Equations II: Goal--Oriented A Posteriori Error Estimation | ||||||||||||
Authors: |
| ||||||||||||
Date: | 2006 | ||||||||||||
Journal or Publication Title: | International Journal of Numerical Analysis & Modeling | ||||||||||||
Open Access: | Yes | ||||||||||||
Gold Open Access: | No | ||||||||||||
In SCOPUS: | No | ||||||||||||
In ISI Web of Science: | No | ||||||||||||
Volume: | 3 | ||||||||||||
Page Range: | pp. 141-162 | ||||||||||||
Status: | Published | ||||||||||||
Keywords: | Discontinuous Galerkin methods, a posteriori error estimation, adaptivity, compressible Navier--Stokes equations | ||||||||||||
HGF - Research field: | Aeronautics, Space and Transport | ||||||||||||
HGF - Program: | Aeronautics | ||||||||||||
HGF - Program Themes: | Aircraft Research (old) | ||||||||||||
DLR - Research area: | Aeronautics | ||||||||||||
DLR - Program: | L AR - Aircraft Research | ||||||||||||
DLR - Research theme (Project): | L - Concepts & Integration (old) | ||||||||||||
Location: | Braunschweig | ||||||||||||
Institutes and Institutions: | Institute of Aerodynamics and Flow Technology > CASE | ||||||||||||
Deposited By: | Hartmann, Dr.rer.nat. Ralf | ||||||||||||
Deposited On: | 21 Jul 2006 | ||||||||||||
Last Modified: | 31 Jul 2019 19:17 |
Repository Staff Only: item control page