A New Stabilized Finite Element Method for Optimal Control for a Ladyzhenskaya Model for Unsteady Flows

作者：Gao Zhiming^*; Kong Fande; Ma Yichen

来源：Numerical Methods for Partial Differential Equations, 2012, 28(1): 263-287.

DOI：10.1002/num.20618

• gradient algorithm
• Ladyzhenskaya model
• optimal control
• optimality condition
• stabilized finite element method

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.

• 出版日期2012-1
• 单位西安交通大学