# Article

 Title: Numerical analysis of a Stokes interface problem based on formulation using the characteristic function (English) Author: Sugitani, Yoshiki Language: English Journal: Applications of Mathematics ISSN: 0862-7940 (print) ISSN: 1572-9109 (online) Volume: 62 Issue: 5 Year: 2017 Pages: 459-476 Summary lang: English . Category: math . Summary: Numerical analysis of a model Stokes interface problem with the homogeneous Dirichlet boundary condition is considered. The interface condition is interpreted as an additional singular force field to the Stokes equations using the characteristic function. The finite element method is applied after introducing a regularization of the singular source term. Consequently, the error is divided into the regularization and discretization parts which are studied separately. As a result, error estimates of order $h^{1/2}$ in $H^1\times L^2$ norm for the velocity and pressure, and of order $h$ in $L^2$ norm for the velocity are derived. Those theoretical results are also verified by numerical examples. (English) Keyword: interface problem Keyword: Stokes equation Keyword: finite element method MSC: 65N15 MSC: 65N30 MSC: 74A50 MSC: 74F10 MSC: 76D07 idZBL: Zbl 06819516 idMR: MR3722899 DOI: 10.21136/AM.2017.0357-16 . Date available: 2017-10-31T08:59:43Z Last updated: 2020-07-02 Stable URL: http://hdl.handle.net/10338.dmlcz/146916 . Reference: [1] Adams, R. A., Fournier, J. J. F.: Sobolev Spaces.Pure and Applied Mathematics 140, Academic Press, New York (2003). Zbl 1098.46001, MR 2424078 Reference: [2] Boffi, D., Gastaldi, L., Heltai, L.: Numerical stability of the finite element immersed boundary method.Math. Models Methods Appl. Sci. 17 (2007), 1479-1505. Zbl 1186.76661, MR 2359913, 10.1142/S0218202507002352 Reference: [3] Boffi, D., Gastaldi, L., Heltai, L., Peskin, C. S.: On the hyper-elastic formulation of the immersed boundary method.Comput. Methods Appl. Mech. Eng. 197 (2008), 2210-2231. 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