Analysis of Continuous \(H^{-1}\)-Least-Squares Methods for the Steady Navier–Stokes System

  • Jérome Lemoine
  • Arnaud MünchEmail author
  • Pablo Pedregal


We analyze two \(H^{-1}\)-least-squares methods for the steady Navier–Stokes system of incompressible viscous fluids. Precisely, we show the convergence of minimizing sequences for the least-squares functional toward solutions. Numerical experiments support our analysis.


Steady Navier–Stokes system Least-squares approach Gradient method 

Mathematics Subject Classification

35Q30 93E24 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Jérome Lemoine
    • 1
  • Arnaud Münch
    • 1
    Email author
  • Pablo Pedregal
    • 2
  1. 1.Laboratoire de MathématiquesUniversité Clermont Auvergne, UMR CNRS 6620AubièreFrance
  2. 2.INEI, Universidad de Castilla La ManchaCiudad RealSpain

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