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Luo Z D, Xie Z H, Shang Y Q, et al. A reduced finite volume element formulation and numerical simulations based on POD for parabolic equations[J]. Journal of Computational and Applied Mathematics, 2011, 235(8): 2098−2111.

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• 标题: Burgers方程基于POD方法的降维CN有限元外推算法 A Reduced-Order CN Finite Element Extrapolating Algorithm Based on POD for Burgers Equation

  作者: 李宏, 黄春霞, 罗振东

  关键字: 二维Burgers方程, 特征投影分解方法, Crank-Nicolson有限元降维外推算法, 误差估计 Two-Dimensional Burgers Equation; Proper Orthogonal Decomposition Technique; Crank-Nicolson Finite Element Reduced-Order Extrapolating Algorithm; Error Estimate

  期刊名称: 《International Journal of Fluid Dynamics》, Vol.1 No.1, 2013-03-22

  摘要: 建立二维Burgers方程基于特征投影分解(POD)方法的时间二阶精度的Crank-Nicolson (CN)有限元降维外推算法，给出这种算法的误差估计，并用误差估计作为算法的POD基数目选取及POD更新的准则。最后用数值实验说明该算法的优越性，这表明了该算法对于求解二维Burgers方程的数值解是有效可行的。 A Crank-Nicolson (CN) finite element reduced-order extrapolating algorithm with second-order accuracy based on proper orthogonal decomposition (POD) technique is established for two-dimensional Burgers equation, its error estimates are provided for criterions of the CN finite element reduced-order extrapolating algorithm to choose the number of POD basis and to renew POD basis. Some numerical experiments are used to show that the advantage of the CN finite element reduced-order extrapolating algorithm. It is shown that the CN finite element reduced-order extrapolating algorithm based on POD technique is feasible and efficient for finding the numerical solutions for two-dimensional Burgers equation.