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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
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