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Operator splitting for two-dimensional incompressible fluid equations

Authors: Helge Holden, Kenneth H. Karlsen and Trygve Karper
Journal: Math. Comp. 82 (2013), 719-748
MSC (2010): Primary 76U05; Secondary 65M12
Published electronically: June 27, 2012
MathSciNet review: 3008836
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Abstract: 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.

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Additional Information

Helge Holden
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway, and Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO–0316 Oslo, Norway

Kenneth H. Karlsen
Affiliation: Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO–0316 Oslo, Norway

Trygve Karper
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway

Keywords: Quasi-geostrophic equation, operator splitting, convergence
Received by editor(s): February 8, 2011
Received by editor(s) in revised form: September 26, 2011
Published electronically: June 27, 2012
Additional Notes: This work was supported in part by the Research Council of Norway.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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