Finite element formulation based on proper orthogonal decomposition for parabolic equations |
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Authors: | ZhenDong Luo Jing Chen Ping Sun XiaoZhong Yang |
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Institution: | (1) School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China;(2) School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, China;(3) College of Science, China Agricultural University, Beijing, 100083, China |
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Abstract: | A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations
so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced
POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations
are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency
of POD method.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10871022, 10771065, and 60573158) and
Natural Science Foundation of Hebei Province (Grant No. A2007001027) |
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Keywords: | proper orthogonal decomposition finite element formulation parabolic equations error analysis |
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