数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1765-1785.doi: 10.1016/S0252-9602(11)60360-3

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A REDUCED MFE FORMULATION BASED ON POD FOR THE NON-STATIONARY CONDUCTION-CONVECTION PROBLEMS

罗振东*|谢正辉|陈静   

  1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China|LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China|College of Sciences, China Agricultural University, Beijing 100083, China
  • 收稿日期:2010-06-09 修回日期:2010-10-13 出版日期:2011-09-20 发布日期:2011-09-20
  • 通讯作者: 罗振东 E-mail:zhdluo@163.com; zxie@lasg.iap.ac.cn; jing quchen@163.com
  • 基金资助:

    Research of this work was supported by the National Science Foundation of China (10871022; 11061009; 40821092); the National Basic Research Program (2010CB428403; 2009CB421407; 2010CB951001); Natural Science Foundation of Hebei Province (A2010001663); and Chinese Universities Scientific Fund (2009-2-05).

A REDUCED MFE FORMULATION BASED ON POD FOR THE NON-STATIONARY CONDUCTION-CONVECTION PROBLEMS

 LUO Zhen-Dong*, XIE Zheng-Hui, CHEN Jing   

  1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China|LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China|College of Sciences, China Agricultural University, Beijing 100083, China
  • Received:2010-06-09 Revised:2010-10-13 Online:2011-09-20 Published:2011-09-20
  • Contact: LUO Zhen-Dong E-mail:zhdluo@163.com; zxie@lasg.iap.ac.cn; jing quchen@163.com
  • Supported by:

    Research of this work was supported by the National Science Foundation of China (10871022; 11061009; 40821092); the National Basic Research Program (2010CB428403; 2009CB421407; 2010CB951001); Natural Science Foundation of Hebei Province (A2010001663); and Chinese Universities Scientific Fund (2009-2-05).

摘要:

In this article, a reduced mixed finite element (MFE) formulation based on proper orthogonal decomposition (POD) for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based
on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.

关键词: proper orthogonal decomposition, mixed finite element formulation, error estimate, non-stationary conduction-convection problems

Abstract:

In this article, a reduced mixed finite element (MFE) formulation based on proper orthogonal decomposition (POD) for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based
on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.

Key words: proper orthogonal decomposition, mixed finite element formulation, error estimate, non-stationary conduction-convection problems

中图分类号: 

  • 65N30