Finite element approximation of a Cahn-Hilliard-Navier-Stokes system

D. Kay, V. Styles and R. Welford

abstract

We consider a semi-discrete and a practical fully-discrete finite element approximation of a Cahn - Hilliard - Navier - Stokes system. This system arises in the modelling of multiphase fluid systems. We show order h error estimate between the solution of the system and the solution of the semi-discrete approximation. We also show the convergence of the fully discrete approximation. Finally, we present an efficient implementation of the fully discrete scheme together with some numerical simulations.

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