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

 

Convergence analysis of a class of massively parallel direction splitting algorithms for the Navier-Stokes equations in simple domains


Authors: Jean-Luc Guermond, Peter D. Minev and Abner J. Salgado
Journal: Math. Comp. 81 (2012), 1951-1977
MSC (2010): Primary 65N12, 65N15, 35Q30
Published electronically: April 13, 2012
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Abstract: We provide a convergence analysis for a new fractional time-stepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization.


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Additional Information

Jean-Luc Guermond
Affiliation: Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, Texas 77843-3368. On leave from CNRS, France
Email: guermond@math.tamu.edu

Peter D. Minev
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta Canada T6G 2G1
Email: minev@ualberta.ca

Abner J. Salgado
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: abnersg@math.umd.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02588-9
PII: S 0025-5718(2012)02588-9
Keywords: Navier-Stokes, fractional time-stepping, direction splitting
Received by editor(s): January 16, 2011
Received by editor(s) in revised form: June 16, 2011
Published electronically: April 13, 2012
Additional Notes: This material is based upon work supported by the National Science Foundation grants DMS-0713829, by the Air Force Office of Scientific Research, USAF, under grant/contract number FA9550-09-1-0424, and a Discovery grant of the National Science and Engineering Research Council of Canada. This publication is also partially based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST)
The work of P. Minev was also supported by fellowships from the Institute of Applied Mathematics and Computational Science and the Institute of Scientific Computing at Texas A&M University
The work of A.J. Salgado was also been supported by NSF grants CBET-0754983 and DMS-0807811.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.