Burgers方程基于POD方法的降维CN有限元外推算法

Abstract

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.