An alternative least-squares formulation of the Navier-Stokes equations with improved mass conservation

J. J. Heys, E. Lee, T. A. Manteuffel, S. F. McCormick

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


The focus of this paper is on incompressible flows in three dimensions modeled by least-squares finite element methods (LSFEM) and using a novel reformulation of the Navier-Stokes equations. LSFEM are attractive because the resulting discrete equations yield symmetric, positive definite systems of algebraic equations and the functional provides both a local and global error measure. On the other hand, it has been documented for existing reformulations that certain types of boundary conditions and high-aspect ratio domains can yield very poor mass conservation. It has also been documented that improved mass conservation with LSFEM can be achieved by strengthening the coupling between the pressure and velocity. The new reformulation presented here is demonstrated to provide both improved multigrid convergence rates because it is differentially diagonally dominant and improved mass conservation over existing methods because it increases the pressure-velocity coupling along the inflow and outflow boundaries.

Original languageEnglish
Pages (from-to)994-1006
Number of pages13
JournalJournal of Computational Physics
Issue number1
Publication statusPublished - 2007 Sept 10

Bibliographical note

Funding Information:
This work was sponsored by the Department of Energy under Grant Nos. DE-FC02-01ER25479 and DE-FG02-03ER25574, Lawrence Livermore National Laboratory under Contract No. B541045, Sandia National Laboratory under Contract No. 15268, the National Science Foundation under Grant Nos. DMS-0410318, and the Flight Attendant Medical Research Institute.

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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