JournalsifbVol. 10, No. 1pp. 15–43

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

  • Vanessa Styles

    University of Sussex, Brighton, UK
  • David Kay

    University of Sussex, Brighton, United Kingdom
  • Richard Welford

    University of Sussex, Brighton, United Kingdom
Finite element approximation of a Cahn–Hilliard–Navier–Stokes system cover
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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 hh 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. 15–43

DOI 10.4171/IFB/178