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Finite element schemes based on energy-stable approximation for two-fluid flow problems with surface tension. (English) Zbl 1134.76032
Summary: For two-fluid flow problems with surface tension, we present finite element schemes based on energy-stable approximation. In the case of no surface tension, those schemes are unconditionally stable in the energy sense. When there exists surface tension, they are proved to be stable if a quantity remains bounded in the computation. Some numerical results on rising bubble problems show the robustness and applicability of these schemes.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76D45 Capillarity (surface tension) for incompressible viscous fluids
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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