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A new stabilized finite element method for optimal control for a Ladyzhenskaya model for unsteady flows
Author(s) -
Gao Zhiming,
Kong Fande,
Ma Yichen
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20618
Subject(s) - discretization , mathematics , optimal control , finite element method , partial differential equation , ordinary differential equation , control (management) , mathematical optimization , order (exchange) , partial derivative , control theory (sociology) , mathematical analysis , differential equation , computer science , physics , finance , artificial intelligence , economics , thermodynamics
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