# 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

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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.

 [1] F. D’Andrea, R. Vautard. Extratropical low-frequency variability as a low-dimensional problem, I: A simplified model. Quarterly Journal of the Royal Meteorological Society, 2001, 127(574): 1357-1374. [2] V. Thomee. Partial differential equations with numerical methods. Berlin: Springer-Verlag, 2003. [3] 罗振东. 混合有限元方法基础及其应用[M]. 北京: 科学出版社, 2006. [4] K. Kunisch, S. Volkwein. Galerkin proper orthogonal decomposition methods for parabolic problems. Numerische Mathematik, 2001, 90(1): 117-148. [5] 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. [6] 罗振东, 陈静, 谢正辉, 安静, 孙萍. 抛物型方程基于POD方法的时间二阶精度CN有限元降维格式[J]. 中国科学A辑: 数学, 2011, 41(5): 447-460. [7] P. Sun, Z. D. Luo and Y. J. Zhou. Some reduced finite difference schemes based on a proper orthogonal decomposition technique for parabolic equations. Applied Numeri-cal Mathematics, 2010, 60(1-2): 154-164. [8] W. Rudin. Functional and analysis (2nd Edition). New York: McGraw-Hill Companies, 1973.