数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 1076-1098.doi: 10.1016/S0252-9602(13)60065-X

• 论文 • 上一篇    下一篇

A NEW REDUCED-ORDER FVE ALGORITHM BASED ON POD METHOD FOR VISCOELASTIC EQUATIONS

李宏|罗振东*|高骏强   

  1. School of Mathematical Sciences, Inner Mongolia University, Huhhot 010021, China; School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
  • 收稿日期:2012-03-26 修回日期:2012-10-08 出版日期:2013-07-20 发布日期:2013-07-20
  • 通讯作者: 罗振东,zhdluo@163.com E-mail:malhong@imu.edu.cn;zhdluo@163.com; gaojunqiang0320@126.com
  • 基金资助:

    Research of this work was supported by the National Science Foundation of China (12271227, 11061009 and 11061021), Natural Science Foundation of Inner Mongolia (2012MS0106), Science Research Program of Guizhou (GJ[2011]2367), Science Research Program of Inner
    Mongolia Advanced Education (NJ10006), and Special Funds for Co-construction Project of Beijing and North China Electric Power University.

A NEW REDUCED-ORDER FVE ALGORITHM BASED ON POD METHOD FOR VISCOELASTIC EQUATIONS

 LI Hong, LUO Zhen-Dong*, GAO Jun-Qiang   

  1. School of Mathematical Sciences, Inner Mongolia University, Huhhot 010021, China; School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
  • Received:2012-03-26 Revised:2012-10-08 Online:2013-07-20 Published:2013-07-20
  • Contact: LUO Zhen-Dong,zhdluo@163.com E-mail:malhong@imu.edu.cn;zhdluo@163.com; gaojunqiang0320@126.com
  • Supported by:

    Research of this work was supported by the National Science Foundation of China (12271227, 11061009 and 11061021), Natural Science Foundation of Inner Mongolia (2012MS0106), Science Research Program of Guizhou (GJ[2011]2367), Science Research Program of Inner
    Mongolia Advanced Education (NJ10006), and Special Funds for Co-construction Project of Beijing and North China Electric Power University.

摘要:

A proper orthogonal decomposition (POD) technique is used to reduce the finite volume element (FVE) method for two-dimensional (2D) viscoelastic equations. A reduced-order fully discrete FVE algorithm with fewer degrees of freedom and sufficiently high accuracy based on POD method is established. The error estimates of the reduced-order fully discrete FVE solutions and the implementation for solving the reduced-order fully discrete FVE algorithm are provided. Some numerical examples are used to illus-trate that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order fully discrete FVE algorithm is one of the most effective numerical methods by comparing with corresponding numerical results of finite element formulation and finite difference scheme and that the reduced-order fully discrete FVE algorithm based on POD method is feasible and efficient for solving 2D viscoelastic equations.

关键词: proper orthogonal decomposition, finite volume element method, viscoelastic equations, error estimate

Abstract:

A proper orthogonal decomposition (POD) technique is used to reduce the finite volume element (FVE) method for two-dimensional (2D) viscoelastic equations. A reduced-order fully discrete FVE algorithm with fewer degrees of freedom and sufficiently high accuracy based on POD method is established. The error estimates of the reduced-order fully discrete FVE solutions and the implementation for solving the reduced-order fully discrete FVE algorithm are provided. Some numerical examples are used to illus-trate that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order fully discrete FVE algorithm is one of the most effective numerical methods by comparing with corresponding numerical results of finite element formulation and finite difference scheme and that the reduced-order fully discrete FVE algorithm based on POD method is feasible and efficient for solving 2D viscoelastic equations.

Key words: proper orthogonal decomposition, finite volume element method, viscoelastic equations, error estimate

中图分类号: 

  • 65N30