论文标题
Cahn-Hilliard-Navier-Stokes System的脱钩分裂方案的收敛
Convergence of a Decoupled Splitting Scheme for the Cahn-Hilliard-Navier-Stokes System
论文作者
论文摘要
本文致力于分析一种能量稳定的不连续的Galerkin算法，用于在脱钩的分裂框架内求解Cahn-Hilliard-Navier-Stokes方程。我们表明，所提出的方案是可解决的，可以保守的。在CFL条件下获得了订单参数的能量耗散和$ l^\ infty $稳定性。最佳梯度规范和$ l^2 $规范中的先验错误估计得出。稳定性证明和错误分析基于感应参数，不需要对潜在功能进行任何正则化。
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 $L^\infty$ stability of the order parameter are obtained under a CFL condition. Optimal a priori error estimates in the broken gradient norm and in the $L^2$ norm are derived. The stability proofs and error analysis are based on induction arguments and do not require any regularization of the potential function.
