TY - JOUR
T1 - A New Finite Element Approximation of a State-Constrained Optimal Control Problem
AU - Liu , Wenbin
AU - Gong , Wei
AU - Yan , Ningning
JO - Journal of Computational Mathematics
VL - 1
SP - 97
EP - 114
PY - 2009
DA - 2009/02
SN - 27
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8562.html
KW - Optimal control problem, State-constraints, Fourth order variational inequalities, Nonconforming finite element method.
AB - <p style="text-align: justify;">In this paper, we study numerical methods for an optimal control problem with pointwise 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.</p>