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

Authors:
Zhendong Luo;Zhenghui Xie;Yueqiang Shang;Jing Chen
Affiliations:
School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China;College of Science, China Agricultural University, Beijing 100083, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

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.