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腾飞, 孙萍, 罗振东. 抛物型方程基于POD方法的时间二阶中心差的二阶精度简化有限元格式[J]. 计算数学, 2011, 33(4): 373-386.

被以下文章引用:

• 标题: 抛物方程基于POD的降阶外推有限元格式A POD-Based Reduced-Order Extrapolating Finite Element Formulation for Parabolic Equations

  作者: 腾飞, 孙萍, 罗振东

  关键字: 特征投影分解方法, 降阶外推有限元格式, 误差估计 Proper Orthogonal Decomposition (POD) Technique; Reduced-Order Extrapolating Finite Element Formulation; Error Estimate

  期刊名称: 《Advances in Applied Mathematics》, Vol.2 No.3, 2013-07-29

  摘要: 用特征投影分解(Proper Orthogonal Decomposition，简记POD)方法去建立二维抛物方程的一种基于POD的时间二阶精度的降阶外推有限元格式；并给出误差估计和求解这种降阶外推有限元格式的算法实现。最后用数值例子验证这种基于POD方法降阶外推有限元格式的可行性和有效性。 A POD-based reduced-order extrapolating finite element formulation with second-order time accuracy for two-dimensional parabolic equations is established by using the proper orthogonal decomposition (POD) technique, and the algorithm implementation of error estimation and solution for POD-based reduced- order extrapolating finite element formulation is provided. Finally, a numerical example is used to verify the feasibility and efficiency of the POD-based reduced-order extrapolating finite element formulation method.