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Error estimation and hp–adaptive mesh refinement for discontinuous Galerkin methods

Leicht, Tobias and Hartmann, Ralf (2011) Error estimation and hp–adaptive mesh refinement for discontinuous Galerkin methods. In: Advances in Computational Fluid Dynamics, 2. World Scientific Books. pp. 67-94. ISBN 978-981-4313-18-6.

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Official URL: http://www.worldscibooks.com/mathematics/7792.html


We present adjoint-based techniques to estimate the error of a numerical flow solution with respect to a given target quantity like an aerodynamic force coefficient. This estimate can be used to judge the overall accuracy of a computation, to enhance the computed value of the target quantity and to drive a solution-adaptive mesh refinement process. The error estimation procedure is extended to multiple target quantities. The discontinuous ansatz spaces of the DG discretization allow for both element subdivision as well as a local increase of polynomial degrees for increasing the flow resolution. Targeting optimal rates of convergence, a smoothness estimation based on a truncated Legendre series expansion of the solution is employed to locally select the more promising strategy. Numerical examples for inviscid, laminar viscous and turbulent viscous flows demonstrate the efficiency of the proposed algorithms.

Item URL in elib:https://elib.dlr.de/72284/
Document Type:Contribution to a Collection
Title:Error estimation and hp–adaptive mesh refinement for discontinuous Galerkin methods
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Leicht, TobiasTobias.Leicht (at) dlr.deUNSPECIFIED
Hartmann, RalfRalf.Hartmann (at) dlr.deUNSPECIFIED
Date:March 2011
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
Page Range:pp. 67-94
Wang, Z.J.Iowa State University, USA
Publisher:World Scientific Books
Series Name:Advances in Computational Fluid Dynamics
Keywords:error estimation hp-adaptivity compressible flow
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:other
HGF - Program Themes:other
DLR - Research area:Aeronautics
DLR - Program:L - no assignment
DLR - Research theme (Project):L - no assignment (old)
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > CASE
Deposited By: Leicht, Tobias
Deposited On:05 Dec 2011 12:59
Last Modified:09 Jun 2017 22:08

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