A reduced finite volume element formulation and numerical simulations based on POD for parabolic problems

作者：Luo, Zhendong^*; Xie, Zhenghui; Shang, Yueqiang; Chen, Jing

来源：Journal of Computational and Applied Mathematics, 2011, 235(8): 2098-2111.

DOI：10.1016/j.cam.2010.10.008

• Proper orthogonal decomposition
• Finite volume element method
• Numerical simulation
• Parabolic equation

A proper orthogonal decomposition (POD) method is applied to a usual finite volume element (FVE) formulation for parabolic equations such that it is reduced to a POD FVE formulation with lower dimensions and high enough accuracy. The error estimates between the reduced POD FVE solution and the usual FVE solution are analyzed. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is also shown that the reduced POD FVE formulation based on POD method is both feasible and highly efficient.

• 出版日期2011-2-15
• 单位贵州师范大学; 华北电力大学; 中国农业大学; 中国科学院大气物理研究所