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Finite element approximation of a Cahn-Hilliard-Navier-Stokes system. (English) Zbl 1144.35043
The author considers a semi-discrete finite element approximation of a Cahn-Hilliard-Navier-Stokes system. This system arises in the modelling of multiphase fluid systems. An order $$h$$ error estimate between the solution of the system and the solution of the semi-discrete approximation is obtained. The convergence of fully discrete approximation is demonstrated. The effectiveness of this approach is illustrated by a numerical example.

##### MSC:
 35Q30 Navier-Stokes equations 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 76M10 Finite element methods applied to problems in fluid mechanics
##### Keywords:
Cahn-Hilliard-Navier-Stokes system; multiphase fluid
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