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We analyze two $$H^{-1}$$ 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.

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