A fully space-time least-squares method for the unsteady Navier-Stokes system
Optimization and Control
2019-09-12 v1 Numerical Analysis
Numerical Analysis
Abstract
We introduce and analyze a space-time least-squares method associated to 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 iterates related to the value of the viscosity constant, 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 when used to solve the Navier-Stokes system through a variational formulation.
Cite
@article{arxiv.1909.05034,
title = {A fully space-time least-squares method for the unsteady Navier-Stokes system},
author = {Jerome Lemoine and Arnaud Munch},
journal= {arXiv preprint arXiv:1909.05034},
year = {2019}
}