Adaptive Mixed Least Squares Galerkin/Petrov Finite Element Method for the Stationary Conduction Convection Problems

ZHANG Yun-zhang; HOU Yan-ren; WEI Hong-bo

doi:10.3879/j.issn.1000-0887.2011.10.005

Volume 32 Issue 10

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ZHANG Yun-zhang, HOU Yan-ren, WEI Hong-bo. Adaptive Mixed Least Squares Galerkin/Petrov Finite Element Method for the Stationary Conduction Convection Problems[J]. Applied Mathematics and Mechanics, 2011, 32(10): 1182-1198. doi: 10.3879/j.issn.1000-0887.2011.10.005

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Adaptive Mixed Least Squares Galerkin/Petrov Finite Element Method for the Stationary Conduction Convection Problems

doi: 10.3879/j.issn.1000-0887.2011.10.005

School of Science, Xi'an Jiaotong University, Xi'an 710049, P. R. China;
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, He'nan 471003, P. R. China

Received Date: 2011-02-21
Rev Recd Date: 2011-06-10
Publish Date: 2011-10-15

Abstract

Abstract

An adaptive mixed least squares Galerkin/Petrov finite element method was developed for the stationary conduction convection problems.The mixed least squares Galerkin/Petrov finite element method was consistent and stable for any combination of discrete velocity and pressure spaces (without requiring a Babuška-Brezzi stability condition).Using the general theory of Verfürth,the a posteriori error estimates of residual type are derived for the problems.Finally,some numerical tests are presented to illustrate the method's efficiency.
- conduction convection problems,
- posteriori error analysis,
- mixed finite element,
- adaptive finite element,
- least squares Galerkin/Petrov method