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

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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 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. © European Mathematical Society 2008.

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Kay, D., Styles, V., & Welford, R. (2008). Finite element approximation of a Cahn-Hilliard-Navier-Stokes system. Interfaces and Free Boundaries, 10(1), 15–43. https://doi.org/10.4171/IFB/178

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