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Analysis of a discontinuous Galerkin approximation of the Stokes problem based on an artificial compressibility flux
Author(s) -
Di Pietro Daniele A.
Publication year - 2007
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1495
Subject(s) - discretization , discontinuous galerkin method , inviscid flow , compressibility , mathematics , flux (metallurgy) , computation , convergence (economics) , finite element method , numerical analysis , mathematical analysis , incompressible flow , flow (mathematics) , physics , classical mechanics , mechanics , geometry , algorithm , materials science , economics , metallurgy , thermodynamics , economic growth
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/ c 2 )(∂ 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. Copyright © 2007 John Wiley & Sons, Ltd.