# 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

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.

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[63] 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.

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