SIAM Journal on Control and Optimization
Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem
Computational Optimization and Applications
Superconvergence Properties of 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
Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems
Computational Optimization and Applications
On finite element error estimates for optimal control problems with elliptic PDEs
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
| Hi-index | 0.00 |
We continue the discussion of error estimates for the numerical analysis of Neumann boundary control problems we started in Casas et al. (Comput. Optim. Appl. 31:193---219, 2005). In that paper piecewise constant functions were used to approximate the control and a convergence of order O(h) was obtained. Here, we use continuous piecewise linear functions to discretize the control and obtain the rates of convergence in L 2(Γ). Error estimates in the uniform norm are also obtained. We also discuss the approach suggested by Hinze (Comput. Optim. Appl. 30:45---61, 2005) as well as the improvement of the error estimates by making an extra assumption over the set of points corresponding to the active control constraints. Finally, numerical evidence of our estimates is provided.