Operator splitting for two-dimensional incompressible fluid equations

We analyze splitting algorithms for a class of two-dimensional fluid equations, which includes the incompressible Navier-Stokes equations and the surface quasi-geostrophic equation. Our main result is that the Godunov and Strang splitting methods converge with the expected rates provided the initial...

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Bibliographic Details
Published in:Mathematics of computation 2013-04, Vol.82 (282), p.719-748
Main Authors: HOLDEN, HELGE, KARLSEN, KENNETH H., KARPER, TRYGVE
Format: Article
Language:English
Subjects:
Approximation
Curl
Error rates
Evolution equations
Incompressible fluids
Integers
Mathematics
Navier Stokes equation
Numerical methods
Scalars
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Description
Summary:We analyze splitting algorithms for a class of two-dimensional fluid equations, which includes the incompressible Navier-Stokes equations and the surface quasi-geostrophic equation. Our main result is that the Godunov and Strang splitting methods converge with the expected rates provided the initial data are sufficiently regular.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-2012-02626-3