An efficient least-squares finite element method for incompressible flows and transport processes

L. Q. Tang, T. T.H. Tsang

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


A numerical procedure based on a least-squares finite clement method (LSFEM) and Jacobi conjugate gradient method (JCG) is presented for the numerical solution of fluid flow and transport problems. Unlike many finite element methods, the LSFEM does not involve any upwinding factor. Furthermore, the LSFEM leads to a symmetric and positive definite linear system of equations which can be solved satisfactorily by a preconditioned conjugate gradient method. Four examples, lid-driven cavity flow, thermally-driven cavity flow, Rayleigh-Bcnard convection and doubly-diffusive flow, are presented to validate the preconditioned conjugate gradient method. A comparison of the least-squares finite element method and the Galerkin finite element method (G FEM) is also given. Finally, we demonstrate that the least-squares finite element method with the Jacobi conjugate gradient iterative technique is a promising approach to solve three-dimensional fluid flow and transport problems.

Original languageEnglish
Pages (from-to)21-39
Number of pages19
JournalInternational Journal of Computational Fluid Dynamics
Issue number1-2
StatePublished - Jan 1 1995

Bibliographical note

Funding Information:
The work was partially supported by the National Science Foundation (Grant No. ASC-8811171; NSF/KY EPSCoR program). We would like to thank Dr. B. N. Jiang or the NASA Lewis Research Center and Dr. X. C Cai or the Department or Mathematics at the University or Kentucky for useful discussions on preconditioned conjugate gradient iterative methods. We also thank Prof. T. W. Cheng for his participation


  • Iterative Methods
  • Jacobi Conjugate Gradient Method
  • Least-squares Finite Element Method
  • incompressible Flows

ASJC Scopus subject areas

  • Computational Mechanics
  • Aerospace Engineering
  • Condensed Matter Physics
  • Energy Engineering and Power Technology
  • Mechanics of Materials
  • Mechanical Engineering


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