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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
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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
Email: holden@math.ntnu.no

Kenneth H. Karlsen
Affiliation: Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO–0316 Oslo, Norway
Email: kennethk@math.uio.no

Trygve Karper
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway
Email: karper@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02626-3
PII: S 0025-5718(2012)02626-3
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.