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 condition. 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.
@article{arxiv.2210.05625,
title = {Convergence of a Decoupled Splitting Scheme for the Cahn-Hilliard-Navier-Stokes System},
author = {Chen Liu and Rami Masri and Beatrice Riviere},
journal= {arXiv preprint arXiv:2210.05625},
year = {2022}
}