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Numerical analysis of a Stokes interface problem based on formulation using the characteristic function. (English) Zbl 06819516
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.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74A50 Structured surfaces and interfaces, coexistent phases
76D07 Stokes and related (Oseen, etc.) flows
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