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Foundations of Computational Mathematics
Published in: Foundations of Computational Mathematics 1/2018

17-11-2016

Convergence of the Marker-and-Cell Scheme for the Incompressible Navier–Stokes Equations on Non-uniform Grids

Authors: T. Gallouët, R. Herbin, J.-C. Latché, K. Mallem

Published in: Foundations of Computational Mathematics | Issue 1/2018

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Abstract

We prove in this paper the convergence of the Marker-and-Cell scheme for the discretization of the steady-state and time-dependent 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 and, for the time-dependent case, the time step of which tend to zero. We then establish that the limit is a weak solution to the continuous problem.
previous article Discrete Moving Frames on Lattice Varieties and Lattice-Based Multispaces

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Appendix
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Metadata
Title
Convergence of the Marker-and-Cell Scheme for the Incompressible Navier–Stokes Equations on Non-uniform Grids
Authors
T. Gallouët
R. Herbin
J.-C. Latché
K. Mallem
Publication date
17-11-2016
Publisher
Springer US
Published in
Foundations of Computational Mathematics / Issue 1/2018
Print ISSN: 1615-3375
Electronic ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-016-9338-4

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