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Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows

Giani, Stefano; Houston, Paul

Authors

Stefano Giani stefano.giani@nottingham.ac.uk

Paul Houston Paul.Houston@nottingham.ac.uk



Abstract

In this article we consider the construction of general isotropic and anisotropic adaptive mesh refinement strategies, as well as hp-mesh refinement techniques, for the numerical approximation of the compressible Euler and Navier-Stokes equations. To discretize the latter system of conservation laws,
we exploit the (adjoint consistent) symmetric version of the interior penalty discontinuous Galerkin finite element method. The a posteriori error indicators are derived based on employing the dual-weighted-residual approach in order to control 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 adjoint 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 adaptive algorithms will be presented.

Journal Article Type Article
Journal International Journal of Numerical Analysis and Modeling
Electronic ISSN 1705-5105
Peer Reviewed Not Peer Reviewed
APA6 Citation Giani, S., & Houston, P. Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. Manuscript submitted for publication
Publisher URL http://www.math.ualberta.ca/ijnam/AIMS.htm
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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