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Regularization error estimates for distributed control problems in energy spaces
Author(s) -
Neumüller Martin,
Steinbach Olaf
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7021
Subject(s) - regularization (linguistics) , mathematics , regularization perspectives on support vector machines , partial differential equation , backus–gilbert method , mathematical optimization , mathematical analysis , inverse problem , tikhonov regularization , computer science , artificial intelligence
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 targetu ‾ 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 functionsu ‾ ∈ H 0 1 ( Ω ) , 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 targetu ‾ by the state u ϱ .