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The role of the Jacobian in the adaptive discontinuous Galerkin method for the compressible Euler equations

Hartmann, R. (2005) The role of the Jacobian in the adaptive discontinuous Galerkin method for the compressible Euler equations. In: Analysis and Numerics for Conservation Laws 1, 1. Springer Heidelberg, Berlin. ISBN 10-3-540-24834-X.

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Abstract

We provide a full description of the Jacobian to the discontinuous Galerkin discretisation of the compressible Euler equations, one of the key ingredients of the adaptive discontinuous Galerkin methods developed in previous publications. We demonstrate the use of this Jacobian within an implicit solver for the approximation of the (primal) stationary flow problems as well as in the adjoint (dual) problems that occur in the context of a posteriori error estimation and adaptive mesh refinement. In particular, we show that the (stationary) compressible Euler equations can efficiently be solved by the Newton method. Full quadratic Newton convergence is achieved on higher order elements as well as on locally refined meshes.

Document Type:Contribution to a Collection
Additional Information: LIDO-Berichtsjahr=2005,
Title:The role of the Jacobian in the adaptive discontinuous Galerkin method for the compressible Euler equations
Authors:
AuthorsInstitution or Email of Authors
Hartmann, R.UNSPECIFIED
Date:2005
Journal or Publication Title:Analysis and Numerics for Conservation Laws
Refereed publication:Yes
In ISI Web of Science:No
Volume:1
Editors:
EditorsEmail
Warnecke, G.UNSPECIFIED
Publisher:Springer Heidelberg, Berlin
Series Name:1
ISBN:10-3-540-24834-X
Status:Published
Keywords:discontinuous Galerkin method, compressible Euler equations, Jacobian, Newton method
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Concepts & Integration
Location: Köln-Porz , Braunschweig , Göttingen
Institutes and Institutions:Institute of Aerodynamics and Flow Technology
Deposited By: Claudia Grant
Deposited On:09 Oct 2005
Last Modified:14 Jan 2010 19:48

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