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Density results using Stokeslets and a method of fundamental solutions for the Stokes equations. (English) Zbl 1079.76058
Summary: We establish new density results for the trace spaces $${\mathbf H}^{1/2}(\partial\Omega)$$ and $${\mathbf H}_n^{1/2} (\partial\Omega)=\{v\in{\mathbf H}^{1/2}(\partial\Omega): \int_{\partial \Omega}v\cdot n=0\}$$ in terms of Stokeslets, fundamental solutions of Stokes equations. Such density results are used to choose basis functions in the method of fundamental solutions (MFS) for solving boundary value problems for Stokes equations. Numerical simulations are presented for the two-dimensional Dirichlet problem using this MFS method.

##### MSC:
 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76D07 Stokes and related (Oseen, etc.) flows
##### Keywords:
trace spaces; Dirichlet problem
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##### References:
 [1] Alves, C.J.S, Density results for the Helmholtz equation and the MFS, (), 45-50 [2] Alves CJS, Chen CS. The MFS method adapted for a non homogeneous equation. ICES’01 Conference Proceedings in CD ROM; 2001. [3] Bogomolny, A, Fundamental solutions method for elliptic boundary value problems, SIAM J num anal, 22, 644-669, (1985) · Zbl 0579.65121 [4] Chen, G; Zhou, J, Boundary element methods, (1992), Academic Press London [5] Girault, V; Raviart, P, Finite element methods for navier – stokes equations, Springer series in computational mathematics 5, (1986), Springer Berlin [6] Golberg, M.A; Chen, C.S, The method of fundamental solutions for potential, Helmholtz and diffusion problems, (), 105-176 · Zbl 0945.65130 [7] Ingham, D.B, The solution of the two-dimensional Stokes equations, (), 671-678 · Zbl 1086.76532 [8] Fairweather, G; Karageorghis, A, The method of fundamental solutions for elliptic boundary value problems, Adv comp math, 9, 69-95, (1998) · Zbl 0922.65074 [9] Kupradze, V.D; Aleksidze, M.A, The method of functional equations for the approximate solution of certain boundary value problems, USSR comput math mathl phys, 4, 82-126, (1964) · Zbl 0154.17604 [10] Poullikkas, A; Karageorghis, A; Georgiou, G; Ascough, A, The method of fundamental solutions for Stokes flows with a free surface, Num meth part diff eq, 14, 664-678, (1998) · Zbl 0922.76262 [11] Tsai, C.C; Young, D.L; Cheng, A.H.D, Meshless BEM for the three-dimensional Stokes flows, Cmes, 3, 1, 117-128, (2002) · Zbl 1147.76595
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