抛物型方程基于POD方法的时间二阶中心差的时间二阶精度简化有限元格式

本文将特征正交分解(Proper Orthogonal Decomposition,简记为POD)方法应用于抛物型方程通常时间二阶中心差的时间二阶精度有限元格式(简称为通常格式),简化其为一个自由度极少但具有时间二阶精度的有限元格式,并给出简化的时间二阶中心差的时间二阶精度有限元格式(简称为简化格式)解的误差分析.数值...

A REDUCED SECOND ORDER TIME ACCURATE FINITE ELEMENT FORMULATION OF TIME SECOND ORDER CENTRAL DIFFERENCE BASED ON POD APPROACH FOR PARABOLIC EQUATIONS

A proper orthogonal decomposition (POD) method is applied to a usual second order time accurate finite element (SOTAFE) formulation of time second order central difference for parabolic equations so that it is reduced into a SOTAFE formulation of time second order central difference with fewer degrees of freedom. The errors between the reduced SOTAFE solutions of time second order central difference based on POD approach and the usual SOTAFE solutions of time second order central difference are analyzed. Numerical examples show that the reduced SOTAFE formulation of time second order central difference based POD approach can save a lot of degrees of freedom in a way that guarantees a sufficiently small errors between the reduced SOTAFE solutions of time second order central difference based on POD approach and the usual SOTAFE solutions of time second order central difference. Moreover, this verifies the reduced SOTAFE formulation of time order central difference based on POD approach is feasible and efficient solving parabolic equations.