Article

Science in China Series A: Mathematics

, Volume 52, Issue 3, pp 585-596

Finite element formulation based on proper orthogonal decomposition for parabolic equations

  • ZhenDong LuoAffiliated withSchool of Mathematics and Physics, North China Electric Power UniversitySchool of Mathematics and Computer Science, Guizhou Normal University
  • , Jing ChenAffiliated withCollege of Science, China Agricultural University Email author 
  • , Ping SunAffiliated withSchool of Mathematics and Computer Science, Guizhou Normal University
  • , XiaoZhong YangAffiliated withSchool of Mathematics and Physics, North China Electric Power University

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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.

Keywords

proper orthogonal decomposition finite element formulation parabolic equations error analysis

MSC(2000)

65N30 35Q10