On efficient least-squares finite element methods for convection-dominated problems

Po Wen Hsieh, Suh Yuh Yang

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


This paper focuses on the least-squares finite element method and its three variants for obtaining efficient numerical solutions to convection-dominated convection-diffusion problems. The coercivity estimates for the corresponding homogeneous least-squares energy functionals are derived, and based on which error estimates are established. One of the common advantages of these least-squares methods is that the resulting linear system is symmetric and positive definite. Numerical experiments that demonstrate the theoretical analysis of the developed methods are presented. It was observed that the primitive least-squares method performs poorly for convection-dominated problems while the stabilized, streamline diffusion and negatively stabilized streamline diffusion least-squares methods perform considerably better for interior layer problems, and the negatively stabilized streamline diffusion least-squares method is able to better capture the boundary layer behavior when compared with other least-squares methods. But all the least-squares methods do not give reasonable results for problem possessing both interior and boundary layer structures in the solution.

Original languageEnglish
Pages (from-to)183-196
Number of pages14
JournalComputer Methods in Applied Mechanics and Engineering
Issue number1-4
StatePublished - 1 Dec 2009


  • Boundary and interior layers
  • Convection-dominated problems
  • Finite element methods
  • Least-squares
  • Stabilized methods
  • Streamline diffusion


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