In this paper, we consider the numerical solution of damped Boussinesq equation using Ciarlet–Raviart mixed finite element method. An implicit finite difference scheme is used for the time discretization. A priori error estimates are analyzed and stability analysis of the method is shown. We obtain an optimal error estimate in $L^2$ norm with quadratic or higher-order element, for both semi and fully discrete finite element approximations. Finally, numerical examples are given to verify the theoretical results.

中文翻译：

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求解阻尼Boussinesq方程的Ciarlet-Raviart混合有限元方法分析

在本文中，我们考虑使用Ciarlet–Raviart混合有限元方法对阻尼Boussinesq方程进行数值解。隐式有限差分方案用于时间离散化。分析先验误差估计并显示该方法的稳定性分析。我们在${\mathrm{大号}}^2$包含二次或更高阶元素的范数，适用于半离散和完全离散的有限元逼近。最后，通过数值算例验证了理论结果。