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Symmetry 2019, 11(1), 54; https://doi.org/10.3390/sym11010054

New Numerical Method for the Rotation form of the Oseen Problem with Corner Singularity

1
Computing Center of Far-Eastern Branch, Russian Academy of Sciences, Kim-Yu-Chen Str. 65, Khabarovsk 680000, Russia
2
Institute of Applied Mathematics of Far-Eastern Branch, Khabarovsk Division, Russian Academy of Sciences, Dzerzhinsky Str. 54, Khabarovsk 680000, Russia
*
Author to whom correspondence should be addressed.
Received: 18 November 2018 / Revised: 7 December 2018 / Accepted: 12 December 2018 / Published: 5 January 2019
(This article belongs to the Special Issue Finite Elements and Symmetry)
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Abstract

In the paper, a new numerical approach for the rotation form of the Oseen system in a polygon Ω with an internal corner ω greater than 180 on its boundary is presented. The results of computational simulations have shown that the convergence rate of the approximate solution (velocity field) by weighted FEM to the exact solution does not depend on the value of the internal corner ω and equals O ( h ) in the norm of a space W 2 , ν 1 ( Ω ) . View Full-Text
Keywords: Oseen problem; corner singularity; weighted finite element method; preconditioning Oseen problem; corner singularity; weighted finite element method; preconditioning
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Rukavishnikov, V.A.; Rukavishnikov, A.V. New Numerical Method for the Rotation form of the Oseen Problem with Corner Singularity. Symmetry 2019, 11, 54.

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