A finite element method for singular solutions of the Navier–Stokes equations on a non-convex polygon
SCIE
SCOPUS
- Title
- A finite element method for singular solutions of the Navier–Stokes equations on a non-convex polygon
- Authors
- Choi, HJ; Kweon, JR
- Date Issued
- 2016-01-15
- Publisher
- Elsevier
- Abstract
- It is shown in Choi and Kweon (2013) that a solution of the Navier-Stokes equations with no-slip boundary condition on a non-convex polygon can be written as [u, p] = C-1[Phi(1), phi(1)]+C-2[Phi(2), phi(2)]+[u(R), p(R)] near each non-convex vertex, where [u(R), p(R)] is an element of H-2 x H-1, [Phi(i), phi(i)] are corner singularity functions for the Stokes problem with no-slip condition, and C-i is an element of R are coefficients which are called the stress intensity factors. We design a finite element method to approximate the coefficients C-i and the regular part [u(R), p(R)], show the unique existence of the approximations, and derive their error estimates. Some numerical examples are given, confirming convergence rates for the approximations. (C) 2015 Elsevier B.V. All rights reserved.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/26649
- DOI
- 10.1016/J.CAM.2015.07.006
- ISSN
- 0377-0427
- Article Type
- Article
- Citation
- Journal of Computational and Applied Mathematics, vol. 292, page. 342 - 362, 2016-01-15
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