TY - JOUR
T1 - Variational Discretization of a Control-Constrained Parabolic Bang-Bang Optimal Control Problem
AU - Daniels , Nikolaus von
AU - Hinze , Michael
JO - Journal of Computational Mathematics
VL - 1
SP - 14
EP - 40
PY - 2020
DA - 2020/02
SN - 38
DO - http://doi.org/10.4208/jcm.1805-m2017-0171
UR - https://global-sci.org/intro/article_detail/jcm/13683.html
KW - Optimal control, Heat equation, Control constraints, Finite elements, A-priori error estimates, Bang-bang controls.
AB - <p style="text-align: justify;"><span style="font-size: 20px;">We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the adjoint equation, we apply Petrov-Galerkin schemes in time and usual conforming finite elements in space. We prove a-priori estimates for the error between the discretized regularized problem and the limit problem. Since these estimates are not robust if the regularization parameter tends to zero, we establish robust estimates, which — depending on the problem&#39;s regularity — enhance the previous ones. In the special case of bang-bang solutions, these estimates are further improved. A numerical example confirms our analytical findings.</span></p>