Control of an elliptic problem with pointwise state constraints
SIAM Journal on Control and Optimization
Boundary control of semilinear elliptic equations with pointwise state constraints
SIAM Journal on Control and Optimization
Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
SIAM Journal on Control and Optimization
Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems
SIAM Journal on Control and Optimization
A variational discretization concept in control constrained optimization: the linear-quadratic case
Computational Optimization and Applications
Journal of Computational Physics
Optimal Control of PDEs with Regularized Pointwise State Constraints
Computational Optimization and Applications
Feasible and Noninterior Path-Following in Constrained Minimization with Low Multiplier Regularity
SIAM Journal on Control and Optimization
Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems
SIAM Journal on Control and Optimization
Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem
SIAM Journal on Numerical Analysis
Adaptive Finite Elements for Elliptic Optimization Problems with Control Constraints
SIAM Journal on Control and Optimization
Adaptivity with Dynamic Meshes for Space-Time Finite Element Discretizations of Parabolic Equations
SIAM Journal on Scientific Computing
On two numerical methods for state-constrained elliptic control problems
Optimization Methods & Software
Goal-Oriented Adaptivity in Control Constrained Optimal Control of Partial Differential Equations
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization
SIAM Journal on Optimization
A Priori Mesh Grading for an Elliptic Problem with Dirac Right-Hand Side
SIAM Journal on Numerical Analysis
Duality Based A Posteriori Error Estimation for Quasi-Periodic Solutions Using Time Averages
SIAM Journal on Scientific Computing
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In this paper optimal control problems governed by elliptic semilinear equations and subject to pointwise state constraints are considered. These problems are discretized using finite element methods and a posteriori error estimates are derived assessing the error with respect to the cost functional. These estimates are used to obtain quantitative information on the discretization error as well as for guiding an adaptive algorithm for local mesh refinement. Numerical examples illustrate the behavior of the method.