A reduced finite element formulation based on proper orthogonal decomposition for Burgers equation

Authors:
Zhendong Luo;Yanjie Zhou;Xiaozhong Yang
Affiliations:
School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;Department of Mathematics and Physics, Beijing Technology and Business University, Beijing 100037, China;School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for Burgers equation such 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 computation are consistent with theoretical conclusions. Moreover, this validates the feasibility and efficiency of the POD method.