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Symmetric Interior Penalty DG Methods for the Compressible Navier--Stokes Equations II: Goal--Oriented A Posteriori Error Estimation

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.

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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:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Hartmann, RalfUNSPECIFIEDUNSPECIFIED
Houston, PaulUniversity of NottinghamUNSPECIFIED
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

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