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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.

MSC:
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
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