论文标题
非平稳性BousSinesQ方程的全差异虚拟元素方法
A fully-discrete virtual element method for the nonstationary Boussinesq equations
论文作者
论文摘要
在目前的工作中，我们提出并分析了一个完全耦合的虚拟元素方法，用于根据流函数和温度场来求解二维非平稳的Boussinesq系统。空间变量的离散化基于耦合$ c^1 $ - 和$ c^0 $ - 控件虚拟元素方法，而向后的欧拉方案则用于时间变量。提供了完全差异问题的适应性和无条件的稳定性。此外，分别针对流函数和温度得出了$ h^2 $ - 和$ h^1 $ norms的错误估计。最后，报告了一组基准测试，以确认理论误差边界并说明了完全差异方案的行为。
In the present work we propose and analyze a fully coupled virtual element method of high order for solving the two dimensional nonstationary Boussinesq system in terms of the stream-function and temperature fields. The discretization for the spatial variables is based on the coupling $C^1$- and $C^0$-conforming virtual element approaches, while a backward Euler scheme is employed for the temporal variable. Well-posedness and unconditional stability of the fully-discrete problem is provided. Moreover, error estimates in $H^2$- and $H^1$-norms are derived for the stream-function and temperature, respectively. Finally, a set of benchmark tests are reported to confirm the theoretical error bounds and illustrate the behavior of the fully-discrete scheme.
