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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (10): 1269-1286.doi: https://doi.org/10.1007/s10483-011-1499-6

• Articles • 上一篇    下一篇

Adaptive mixed least squares Galerkin/Petrov finite element method for stationary conduction convection problems

张运章1,2 侯延仁1 魏红波1   

  1. 1. School of Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China;
    2. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, Henan Province, P. R. China
  • 收稿日期:2011-02-21 修回日期:2011-06-10 出版日期:2011-10-09 发布日期:2011-10-09

Adaptive mixed least squares Galerkin/Petrov finite element method for stationary conduction convection problems

ZHANG Yun-Zhang1,2, HOU Yan-Ren1, WEI Hong-Bo1   

  1. 1. School of Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China;
    2. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, Henan Province, P. R. China
  • Received:2011-02-21 Revised:2011-06-10 Online:2011-10-09 Published:2011-10-09

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被引次数

7

摘要： An adaptive mixed least squares Galerkin/Petrov finite element method (FEM) is developed for stationary conduction convection problems. The mixed least squares Galerkin/Petrov FEM is consistent and stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. Using the general theory of Verf¨urth, the posteriori error estimates of the residual type are derived. Finally, numerical tests are presented to illustrate the effectiveness of the method.

Abstract: An adaptive mixed least squares Galerkin/Petrov finite element method (FEM) is developed for stationary conduction convection problems. The mixed least squares Galerkin/Petrov FEM is consistent and stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. Using the general theory of Verf¨urth, the posteriori error estimates of the residual type are derived. Finally, numerical tests are presented to illustrate the effectiveness of the method.

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