, Volume 52, Issue 3, pp 585-596
Date: 15 Mar 2009

Finite element formulation based on proper orthogonal decomposition for parabolic equations

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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.