Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Spectral representations, and approximations, of divergence-free vector fields


Authors: Giles Auchmuty and Douglas R. Simpkins
Journal: Quart. Appl. Math. 74 (2016), 429-441
MSC (2010): Primary 35Q35, 35P05, 41A99, 76M22
DOI: https://doi.org/10.1090/qam/1427
Published electronically: June 20, 2016
MathSciNet review: 3518223
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Abstract | References | Similar Articles | Additional Information

Abstract: Special solutions of the equation for a solenoidal vector field subject to prescribed flux boundary conditions are described. A unique gradient solution is found and proved to be the least energy solution of the problem. This solution has a representation in terms of certain $ \Sigma -$$ \mbox {Steklov}-$eigenvalues and eigenfunctions. Error estimates for finite approximations of these solutions are obtained. Some results of computational simulations for two-dimensional and axisymmetrical problems are presented.


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Additional Information

Giles Auchmuty
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3008
Email: auchmuty@uh.edu

Douglas R. Simpkins
Affiliation: Weatherford International, Houston, Texas
Email: SimpkinsDouglas@yahoo.com

DOI: https://doi.org/10.1090/qam/1427
Received by editor(s): December 29, 2014
Published electronically: June 20, 2016
Additional Notes: The research of the first author was partially supported by NSF award DMS 11008754
Article copyright: © Copyright 2016 Brown University


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