Control of an elliptic problem with pointwise state constraints
SIAM Journal on Control and Optimization
Augemented Lagrangian Techniques for Elliptic State Constrained Optimal Control Problems
SIAM Journal on Control and Optimization
Primal-Dual Strategy for State-Constrained Optimal Control Problems
Computational Optimization and Applications
A level set approach for the solution of a state-constrained optimal control problem
Numerische Mathematik
Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem
SIAM Journal on Numerical Analysis
Computational Optimization and Applications
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An integral state-constrained optimal control problem governed by an elliptic partial differential equation and its finite element approximation are considered. The finite element approximation is constructed on multimeshes. An $L^2$-norm a priori error estimate of the finite element approximation is obtained. Further, some superconvergence results are proved. Based on these superconvergence results, almost optimal $L^\infty$-norm error estimates are derived. Some recovery algorithms are then proposed to produce a posteriori error estimators of gradient type. To solve the finite element system, a simple and yet efficient iterative gradient projection algorithm is proposed and its convergence rate is proved. Some numerical examples are performed to confirm theoretical analysis.