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DG discretizations for compressible flows: Adjoint consistency analysis, error estimation and adaptivity

Hartmann, Ralf (2007) DG discretizations for compressible flows: Adjoint consistency analysis, error estimation and adaptivity. Adaptive Numerical Methods for PDEs, 2007-06-10 - 2007-06-16, Oberwolfach.

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Official URL: http://www.mfo.de/programme/schedule/2007/24/OWR_2007_29.pdf

Abstract

<strong>1. Adjoint consistency</strong> - in addition to consistency - is the key requirement for discontinuous Galerkin (DG) discretizations to be of optimal order in L<sup>2</sup> as well as measured in terms of target functionals J(.). If the primal and adjoint solutions are sufficiently smooth, the order of convergence in J for an adjoint consistent discretization is twice the order of an adjoint inconsistent discretization (order doubling). In this talk we provide a general framework for analyzing the adjoint consistency of DG discretizations. We collect several conclusions which can be drawn from analyzing the adjoint consistency property of DG discretizations of the linear advection equation, Poisson's equation and the compressible Euler and Navier-Stokes equations. <strong>2. Error estimation and adaptivity:</strong> We give some examples of applying an <em>a posteriori</em> error estimation and adjoint based refinement to inviscid and viscous laminar sub-, trans- and supersonic compressible flows also in combination with anisotropic mesh refinement.

Item URL in elib:https://elib.dlr.de/50726/
Document Type:Conference or Workshop Item (Paper)
Title:DG discretizations for compressible flows: Adjoint consistency analysis, error estimation and adaptivity
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Hartmann, RalfUNSPECIFIEDUNSPECIFIED
Date:2007
Refereed publication:No
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Volume:29/200
Page Range:pp. 26-30
Editors:
EditorsEmail
Mathematisches Forschungsinstitut Oberwolfach, UNSPECIFIED
Series Name:Oberwolfach Report
Status:Published
Keywords:Adjoint consistency analysis, error estimation, adaptive mesh refinement
Event Title:Adaptive Numerical Methods for PDEs
Event Location:Oberwolfach
Event Type:international Conference
Event Dates:2007-06-10 - 2007-06-16
Organizer:R. Rannacher, E. Süli, and R. Verführt
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:09 Jan 2008
Last Modified:31 Jul 2019 19:20

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