University of Tabriz Computational Methods for Differential Equations 2345-3982 3 2 2015 04 01 Optimization with the time-dependent Navier-Stokes equations as constraints 87 98 4484 EN Mitra Vizheh Department of Mathematics, Shahed University, Tehran, P.O. Box: 18151-159, Iran Syaed Hodjatollah Momeni-Masuleh Department of Mathematics, Shahed University, Tehran, P.O. Box: 18151-159, Iran Alaeddin Malek Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, P.O. Box: 14115-134, Iran Journal Article 2015 06 06 In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the optimal control of the Navier-Stokes equations is proposed. Numerical examples are given to demonstrate the efficiency of the method. https://cmde.tabrizu.ac.ir/article_4484_0de495e641081aae07a2b511ceceb9bf.pdf