Anisotropic $hp$-Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows
Year: 2012
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 4 : pp. 928–949
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-666
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 4 : pp. 928–949
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Discontinuous Galerkin methods a posteriori error estimation adaptivity anisotropic $hp$-refinement compressible flows.