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A Fully Space-Time Least-Squares Method for the Unsteady Navier–Stokes System

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Abstract

We introduce and analyze a space-time least-squares method associated with the unsteady Navier–Stokes system. Weak solution in the two dimensional case and regular solution in the three dimensional case are considered. From any initial guess, we construct a minimizing sequence for the least-squares functional which converges strongly to a solution of the Navier–Stokes system. After a finite number of iterations related to the value of the viscosity coefficient, the convergence is quadratic. Numerical experiments within the two dimensional case support our analysis. This globally convergent least-squares approach is related to the damped Newton method.

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Funding

The second author is funded by the French government research program “Investissements d’Avenir” through the IDEX-ISITE initiative 16-IDEX-0001 (CAP 20-25)

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Correspondence to Arnaud Münch.

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Communicated by R. Glowinski.

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Lemoine, J., Münch, A. A Fully Space-Time Least-Squares Method for the Unsteady Navier–Stokes System. J. Math. Fluid Mech. 23, 102 (2021). https://doi.org/10.1007/s00021-021-00627-6

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