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 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.
Cite this article
Vanessa Styles, David Kay, Richard Welford, Finite element approximation of a Cahn–Hilliard–Navier–Stokes system. Interfaces Free Bound. 10 (2008), no. 1, pp. 15–43DOI 10.4171/IFB/178