Liu, Steve Wenbin and Gong, Wei and Yan, Ningning (2009) A new finite element approximation of a state-constrained optimal control problem. Journal of Computational Mathematics, 27 (1). pp. 97-114. ISSN 0254-9409. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
In this paper, we study numerical methods for an optimal control problem with point-wise state constraints. The traditional approaches often need to deal with the delta-singularity in the dual equation, which causes many difficulties in its theoretical analysis and numerical approximation. In our new approach we reformulate the state-constrained optimal control as a constrained minimization problems only involving the state, whose optimality condition is characterized by a fourth order elliptic variational inequality. Then direct numerical algorithms (nonconforming finite element approximation) are proposed for the inequality, and error estimates of the finite element approximation are derived. Numerical experiments illustrate the effectiveness of the new approach.
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Social Sciences > Kent Business School|
|Depositing User:||Steve Wenbin Liu|
|Date Deposited:||01 Mar 2010 11:41|
|Last Modified:||23 Jun 2014 10:49|
|Resource URI:||https://kar.kent.ac.uk/id/eprint/22892 (The current URI for this page, for reference purposes)|