Abstract
We prove in this paper the convergence of the Marker and cell (MAC) scheme for the discretization of the steady-state incompressible Navier-Stokes equations in primitive variables on non-uniform Cartesian grids, without any regularity assumption on the solution. A priori estimates on solutions to the scheme are proven; they yield the existence of discrete solutions and the compactness of sequences of solutions obtained with family of meshes the space step of which tends to zero. We then establish that the limit is a weak solution to the continuous problem.
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Herbin, R., Latché, JC., Mallem, K. (2014). Convergence of the MAC Scheme for the Steady-State Incompressible Navier-Stokes Equations on Non-uniform Grids. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_33
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DOI: https://doi.org/10.1007/978-3-319-05684-5_33
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