Convergence analysis of the FEM approximation of the first order projection method for incompressible flows with and without the inf-sup condition |
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Authors: | Santiago Badia Ramon Codina |
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Institution: | (1) Universitat Politècnica de Catalunya, Jordi Girona 1-3, Edifici C1, 08034 Barcelona, Spain |
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Abstract: | In this paper we obtain convergence results for the fully discrete projection method for the numerical approximation of the
incompressible Navier–Stokes equations using a finite element approximation for the space discretization. We consider two
situations. In the first one, the analysis relies on the satisfaction of the inf-sup condition for the velocity-pressure finite
element spaces. After that, we study a fully discrete fractional step method using a Poisson equation for the pressure. In
this case the velocity-pressure interpolations do not need to accomplish the inf-sup condition and in fact we consider the
case in which equal velocity-pressure interpolation is used. Optimal convergence results in time and space have been obtained
in both cases. |
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Keywords: | 35Q30 65M12 65M60 |
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