For tracking type distributed optimal control problems subject to second-order elliptic partial differential equations, we analyze the regularization error of the state u ϱ and the target (Formula presented.) with respect to the regularization parameter ϱ. The main focus is on the regularization in the energy space H −1(Ω), but we also consider the regularization in L 2(Ω) for comparison. While there is no difference in the regularization error estimates when considering suitable target functions (Formula presented.), we obtain a higher-order convergence in the relaxation parameter ϱ when considering the control in the energy space H −1(Ω), which also affects the approximation of the target (Formula presented.) by the state u ϱ.
- distributed control problem
- regularization error estimates
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- Information, Communication & Computing