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

✍ Scribed by Zhendong Luo; Zhenghui Xie; Yueqiang Shang; Jing Chen

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
921 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

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