Analysis of [H-1, L2, L2] first-order system least squares for the incompressible Oseen type equations

Sang Dong Kim, Yong Hun Lee, Suh Yuh Yang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper is devoted to the error analysis of least-squares finite element approximations to the stationary incompressible Oseen type equations with the homogeneous velocity boundary condition. With the vorticity as a new dependent variable, we consider two first-order system problems for the Oseen type equations in the velocityvorticity-pressure and the velocity-vorticity-Bernoulli pressure formulations. The least-squares functional is defined in terms of the sum of the squared H-1 and L2 norms of the residual equations over a suitable product function space. The well-posedness of the proposed least-squares variational problem is shown. We then analyze the case where the H-1 norm in the least-squares functional is replaced by a discrete functional to make the computation feasible. Optimal error estimates for all unknowns are derived.

Original languageEnglish
Pages (from-to)77-88
Number of pages12
JournalApplied Numerical Mathematics
Issue number1
StatePublished - Jan 2005


  • Finite element methods
  • First-order system least squares
  • Navier-Stokes equations
  • Oseen type equations
  • Velocity-vorticity-Bernoulli pressure formulation
  • Velocity-vorticity-pressure formulation


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