非定常Stokes方程的稳定化CN有限体积元格式
A Stabilized Crank-Nicolson Finite Volume Element Formulation for Non-Stationary Stokes Equation
DOI: 10.12677/IJFD.2013.12005, PDF, HTML,    国家自然科学基金支持
作者: 李 宏, 赵智慧：内蒙古大学数学科学学院，呼和浩特；罗振东*：华北电力大学数理学院，北京
关键词: Stokes方程；稳定化Crank-Nicolson有限体积元格式；误差估计；Stokes Equation; Stabilized Crank-Nicolson Finite Volume Element Formulation; Error Estimate
摘要: 建立二维非定常Stokes方程的时间二阶精度的稳定化Crank-Nicolson (CN)有限体积元格式, 并给出其稳定化CN有限体积元解的误差估计。数值实验说明时间二阶精度的稳定化CN有限体积元格式比时间一阶精度格式更优越, 从而表明稳定化CN有限体积元格式对于求解非定常Stokes方程的数值解是有效可行的。
Abstract: A stabilized Crank-Nicolson (CN) finite volume element formulation with time second-order accuracy is established for two-dimensional non-stationary Stokes equation. The error estimates of its numerical solutions are provided. Some numerical experiments are presented illustrating that the stabilized CN finite volume element formulation with time second-order accuracy is far more advantageous than that with time first-order accuracy, thus validating that the stabilized CN finite volume element formulation is feasible and efficient for finding the numerical solutions for two- dimensional non-stationary Stokes equation.
文章引用：李宏, 赵智慧, 罗振东. 非定常Stokes方程的稳定化CN有限体积元格式[J]. 流体动力学, 2013, 1(2): 26-33. http://dx.doi.org/10.12677/IJFD.2013.12005

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[23] Suli E. Convergence of finite volume schemes for Poisson's equation on no-nuniform meshes [J]. SIAM Journal on Numerical Analysis, 1991, 28 (5): 1419–1430.
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[29] Yang M, Song H L. A post processing finite volume method for time-dependent Stokes equations [J]. Applied Numerical Mathematics, 2009, 59: 1922–1932.
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