SIAM Journal on Numerical Analysis, Volume 61, Issue 6, Page 2651-2694, December 2023.
Abstract. 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 [math] 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 [math] norm are derived. The stability proofs and error analysis are based on induction arguments and do not require any regularization of the potential function.

中文翻译：

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Cahn-Hilliard-Navier-Stokes 系统解耦分裂方案的收敛性

SIAM 数值分析杂志，第 61 卷，第 6 期，第 2651-2694 页，2023 年 12 月。
摘要。本文致力于分析能量稳定的不连续伽辽金算法，用于在解耦分裂框架内求解 Cahn-Hilliard-Navier-Stokes 方程。我们证明了所提出的方案是唯一可解的并且是质量保守的。能量耗散和阶次参数的[数学]稳定性是在类似 CFL 的约束下获得的。导出了破坏梯度范数和[数学]范数中的最佳先验误差估计。稳定性证明和误差分析基于归纳论证，不需要对势函数进行任何正则化。