Analysis of a discontinuous Galerkin approximation of the Stokes problem based on an artificial compressibility flux

Abstract : In this work, we propose and analyse a discontinuous Galerkin (DG) method for the Stokes problem based on an artificial compressibility numerical flux. A crucial step in the definition of a DG method is the choice of the numerical fluxes, which affect both the accuracy and the order of convergence of the method. We propose here to treat the viscous and the inviscid terms separately. The former is discretized using the well‐known BRMPS method. For the latter, the problem is locally modified by adding an artificial compressibility term of the form (1/c2)(∂p/∂t) for the sole purpose of interface flux computation. The flux is obtained as the exact solution of a local Riemann problem. The analysis of the method extends the well‐established strategies for the DG discretization of the Laplacian to the resulting partially coercive problem.
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International Journal for Numerical Methods in Fluids, Wiley, 2007, 55 (8), pp.793 - 813. 〈https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.1495〉. 〈10.1002/fld.1495〉
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https://hal.archives-ouvertes.fr/hal-01818207
Contributeur : Daniele Antonio Di Pietro <>
Soumis le : lundi 18 juin 2018 - 18:24:41
Dernière modification le : jeudi 26 juillet 2018 - 11:10:47

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Daniele Antonio Di Pietro. Analysis of a discontinuous Galerkin approximation of the Stokes problem based on an artificial compressibility flux. International Journal for Numerical Methods in Fluids, Wiley, 2007, 55 (8), pp.793 - 813. 〈https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.1495〉. 〈10.1002/fld.1495〉. 〈hal-01818207〉

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