A priori Error Analysis of a Discontinuous Galerkin Method for Cahn-Hilliard-Navier-Stokes Equations

Abstract

In this paper, we analyze an interior penalty discontinuous Galerkin method for solving the coupled Cahn-Hilliard and Navier-Stokes equations. We prove uncon-ditional unique solvability of the discrete system, and we derive stability bounds without any restrictions on the chemical energy density function. The numerical solutions satisfy a discrete energy dissipation law and mass conservation laws. Convergence of the method is obtained by obtaining optimal a priori error estimates.

Keywords

Cahn-Hilliard-Navier-Stokes / interior penalty discontinuous Galerkin method / ex-istence / uniqueness / stability / error estimates

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