Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal-Oriented a Posteriori Error Estimation
Year: 2006
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 2 : pp. 141–162
Abstract
In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier-Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I a posteriori bounds are derived for the estimation of 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 dual 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 approach will be presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-IJNAM-894
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 2 : pp. 141–162
Published online: 2006-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: discontinuous Galerkin methods a posteriori error estimation adaptivity compressible Navier-Stokes equations.