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A new stabilized finite element method for optimal control for a Ladyzhenskaya model for unsteady flows

✍ Scribed by Zhiming Gao; Fande Kong; Yichen Ma

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
665 KB
Volume
28
Category
Article
ISSN
0749-159X

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✦ Synopsis

Abstract

This article considers the time‐dependent optimal control problem of tracking the velocity for the viscous incompressible flows which is governed by a Ladyzhenskaya equations with distributed control. The existence of the optimal solution is shown and the first‐order optimality condition is established. The semidiscrete‐in‐time approximation of the optimal control problem is also given. The spatial discretization of the optimal control problem is accomplished by using a new stabilized finite element method which does not need a stabilization parameter or calculation of high order derivatives. Finally a gradient algorithm for the fully discrete optimal control problem is effectively proposed and implemented with some numerical examples. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 263–287, 2012

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