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On the convergence of finite element solutions to the interface problem for the Stokes system. (English) Zbl 1100.76036
Summary: The Stokes system with a discontinuous coefficient (Stokes interface problem) and its finite element approximations are considered. We firstly obtain a general error estimate. To derive explicit convergence rates, we introduce some appropriate assumptions on the regularity of exact solutions and on a geometric condition for triangulation. We mainly deal with MINI element approximation, and then consider P1-iso-P2/P1 element approximation. Results are expected to give an instructive remark in numerical analysis for two-phase flow problems.

76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
Full Text: DOI
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