数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (5): 1471-1484.doi: 10.1016/S0252-9602(13)60097-1

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A REDUCED-ORDER MFE FORMULATION BASED ON POD METHOD FOR PARABOLIC EQUATIONS

罗振东*|李磊|孙萍   

  1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China; School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China
  • 收稿日期:2011-05-26 修回日期:2012-10-31 出版日期:2013-09-20 发布日期:2013-09-20
  • 通讯作者: 罗振东,zhdluo@163.com E-mail:zhdluo@163.com;lilei8764@163.com; sunp@gznu.edu.cn
  • 基金资助:

    The research was supported by the National Science Foundation of China (11271127 and 11061009), Science Research Program of Guizhou (GJ[2011]2367), and the Co-Construction Project of Beijing Municipal Commission of Education.

A REDUCED-ORDER MFE FORMULATION BASED ON POD METHOD FOR PARABOLIC EQUATIONS

 LUO Zhen-Dong*, LI Lei, SUN Ping   

  1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China; School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China
  • Received:2011-05-26 Revised:2012-10-31 Online:2013-09-20 Published:2013-09-20
  • Contact: LUO Zhen-Dong,zhdluo@163.com E-mail:zhdluo@163.com;lilei8764@163.com; sunp@gznu.edu.cn
  • Supported by:

    The research was supported by the National Science Foundation of China (11271127 and 11061009), Science Research Program of Guizhou (GJ[2011]2367), and the Co-Construction Project of Beijing Municipal Commission of Education.

摘要:

In this paper, we extend the applications of proper orthogonal decomposition (POD) method, i.e., apply POD method to a mixed finite element (MFE) formulation naturally satisfied Brezz-Babu?ska for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis-tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.

关键词: proper orthogonal decomposition method, mixed finite element formulation, parabolic equation, error estimate

Abstract:

In this paper, we extend the applications of proper orthogonal decomposition (POD) method, i.e., apply POD method to a mixed finite element (MFE) formulation naturally satisfied Brezz-Babu?ska for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis-tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.

Key words: proper orthogonal decomposition method, mixed finite element formulation, parabolic equation, error estimate