A variational discretization concept in control constrained optimization: the linear-quadratic case
Computational Optimization and Applications
Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem
SIAM Journal on Numerical Analysis
Stability of semilinear elliptic optimal control problems with pointwise state constraints
Computational Optimization and Applications
Calcolo: a quarterly on numerical analysis and theory of computation
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We consider an elliptic optimal control problem with pointwise bounds on the gradient of the state. To guarantee the required regularity of the state we include the L r -norm of the control in our cost functional with rd (d=2,3). We investigate variational discretization of the control problem (Hinze in Comput. Optim. Appl. 30:45---63, 2005) as well as piecewise constant approximations of the control. In both cases we use standard piecewise linear and continuous finite elements for the discretization of the state. Pointwise bounds on the gradient of the discrete state are enforced element-wise. Error bounds for control and state are obtained in two and three space dimensions depending on the value of r.