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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (7): 861-874.doi: https://doi.org/10.1007/s10483-013-1713-x

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Superconvergence of nonconforming finite element penalty scheme for Stokes problem using L2 projection method

石东洋1 裴丽芳2   

  1. 1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, P. R. China;
    2. Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang 471003, Henan Province, P. R. China
  • 出版日期:2013-07-03 发布日期:2013-07-03
  • 通讯作者: Dong-yang SHI E-mail:shi_dy@zzu.edu.cn

Superconvergence of nonconforming finite element penalty scheme for Stokes problem using L2 projection method

Dong-yang SHI1, Li-fang PEI2   

  1. 1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, P. R. China;
    2. Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang 471003, Henan Province, P. R. China
  • Online:2013-07-03 Published:2013-07-03
  • Contact: Dong-yang SHI E-mail:shi_dy@zzu.edu.cn

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摘要： A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.

关键词: 阶段结构, 脉冲存放, 连续收获, 全局吸引, 持久, superconvergence, L2 projection method, Crouzeix-Raviart type nonconforming finite element, penalty scheme

Abstract: A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.

Key words: stage-structured, impulsive stocking, continuous harvesting, global attractivity, permanence, L2 projection method, Crouzeix-Raviart type nonconforming finite element, penalty scheme, superconvergence

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