A reduced-order Crank-Nicolson finite volume element formulation based on POD method for parabolic equations

作者：Luo, Zhendong^*; Li, Hong; Sun, Ping

来源：Applied Mathematics and Computation, 2013, 219(11): 5887-5900.

DOI：10.1016/j.amc.2012.11.083

• Proper orthogonal decomposition
• Crank-Nicolson finite volume element formulation
• Error estimate
• Parabolic equation
• Numerical simulation

In this paper, a proper orthogonal decomposition (POD) method is used to deal with a classical Crank-Nicolson finite volume element (CNFVE) method for two-dimensional parabolic equations. A reduced-order CNFVE formulation with lower dimensions and sufficiently high accuracy based on POD technique is established, the error estimates between reduced-order CNFVE solutions based on the POD method and classical CNFVE solutions are provided, and the extrapolation algorithm for solving reduced-order CNFVE formulation is implemented. Some numerical examples show that the results of numerical computation are consistent with previous theoretical conclusions. Moreover, it is shown that the reduced-order CNFVE formulation based on POD method is feasible and efficient for solving two-dimensional parabolic equations.

• 出版日期2013-2-1
• 单位内蒙古大学; 贵州师范大学; 华北电力大学