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

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.