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Family of convergent numerical schemes for the incompressible Navier-Stokes equations

Abstract : This paper presents the common mathematical features which are leading to convergence properties for a family of numerical schemes applied to the discretisation of the steady and transient incompressible Navier-Stokes equations with homogeneous Dirichlet’s boundary conditions. This family includes the Taylor-Hood scheme, the MAC scheme, the Crouzeix-Raviart scheme generalized into the Hybrid Mixed Mimetic scheme, which can be combined with a variety of discretisations for the nonlinear convection term, each of them being more efficient than the others in particular situa- tions. We provide tools for analyzing all the combined methods, and proving their convergence to a weak solution of the problem.
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https://hal.archives-ouvertes.fr/hal-01382924
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Submitted on : Tuesday, August 29, 2017 - 10:42:33 AM
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Robert Eymard, Pierre Feron, Cindy Guichard. Family of convergent numerical schemes for the incompressible Navier-Stokes equations. Mathematics and Computers in Simulation, Elsevier, 2017, ⟨10.1016/j.matcom.2017.08.003⟩. ⟨hal-01382924v2⟩

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