标题： 电流体动力学方程二阶时间有限元方法的最优误差估计 显示英文标题

标题： Optimal error estimates of a second-order temporally finite element method for electrohydrodynamic equations

摘要： 在这项工作中，我们主要提出了求解电流体力学方程的二阶时间有限元格式的最佳收敛率。由于高度耦合的非线性，此类系统的数值格式的收敛性分析相当罕见，更不用说高阶时间格式的最佳误差估计了。为此，我们放弃了传统的跟随能量估计过程的误差分析方法，这可能导致精度损失。相反，我们注意到尽管电荷密度并未出现在能量稳定性分析中，但它确实直接由其控制方程具有“能量”衰减性质。这一事实使我们能够更方便地控制电荷密度的误差项，最终导致最佳收敛率。提供了几个数值例子来证明理论结果，包括能量稳定性、质量守恒和收敛率。 显示英文摘要

摘要： In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the numerical schemes for such a system is rather rare, not to mention the optimal error estimates for the high-order temporally scheme. To this end, we abandon the traditional error analysis method following the process of energy estimate, which may lead to the loss of accuracy. Instead, we note that the charge density also possesses the "energy" decaying property directly derived by its governing equation, although it does not appear in the energy stability analysis. This fact allows us to control the error terms of the charge density more conveniently, which finally leads to the optimal convergence rates. Several numerical examples are provided to demonstrate the theoretical results, including the energy stability, mass conservation, and convergence rates.