CONVERGENCE OF A DECOUPLED SPLITTING SCHEME FOR THE CAHN-HILLIARD-NAVIER-STOKES SYSTEM.

This paper is devoted to the analysis of an energy-stable discontinuous Galerkin algorithm for solving the Cahn-Hilliard-Navier-Stokes equations within a decoupled splitting framework. We show that the proposed scheme is uniquely solvable and mass conservative. The energy dissipation and the L∞ stability of the order parameter are obtained under a CFL-like constraint. Optimal a priori error estimates in the broken gradient norm and in the L² norm are derived. The stability proofs and error analysis are based on induction arguments and do not require any regularization of the potential function. [ABSTRACT FROM AUTHOR]