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Adjoint consistency analysis of Discontinuous Galerkin discretizations

Hartmann, Ralf (2007) Adjoint consistency analysis of Discontinuous Galerkin discretizations. Siam Journal on Numerical Analysis, 45 (6), pp. 2671-2696. SIAM - Society for Industrial and Applied Mathematics. DOI: [10.1137/060665117] ISSN 0036-1429

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Official URL: http://epubs.siam.org/doi/abs/10.1137/060665117

Abstract

This paper is concerned with the adjoint consistency of discontinuous Galerkin (DG) discretizations. Adjoint consistency - in addition to consistency - is the key requirement for DG discretizations to be of optimal order in L<sup>2</sup> as well as measured in terms of target functionals. We provide a general framework for analyzing the adjoint consistency of DG discretizations which is also useful for the derivation of adjoint consistent methods. This analysis will be performed for the DG discretizations of the linear advection equation, the interior penalty DG method for elliptic problems and the DG discretization of the compressible Euler equations. This framework is then used to derive an adjoint consistent DG discretization of the compressible Navier-Stokes equations. Numerical experiments demonstrate the link of adjoint consistency to the accuracy of numerical flow solutions and the smoothness of discrete adjoint solutions.

Item URL in elib:https://elib.dlr.de/50724/
Document Type:Article
Title:Adjoint consistency analysis of Discontinuous Galerkin discretizations
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Hartmann, RalfRalf.Hartmann (at) dlr.deUNSPECIFIED
Date:2007
Journal or Publication Title:Siam Journal on Numerical Analysis
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:45
DOI :[10.1137/060665117]
Page Range:pp. 2671-2696
Publisher:SIAM - Society for Industrial and Applied Mathematics
ISSN:0036-1429
Status:Published
Keywords:Discontinuous Galerkin discretization, adjoint consistency, compressible Navier-Stokes equations, continuous adjoint problem, discrete adjoint problem
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 > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering
Deposited By: Hartmann, Dr.rer.nat. Ralf
Deposited On:09 Jan 2008
Last Modified:06 Sep 2019 15:17

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