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A prior error estimate is considered for the finite element (FE) approximation of a parabolic optimal control (POC) with spatial measurement data. We use conforming linear finite element to discretize the space for the state, piecewise constant for the control, and Euler method to discretize the time. The convergence order O(h2−s2+k12) in the L2(0,T,L2(Ω))-norm of state variable, co-state, and control variable are obtained. To validate our theory, numerical tests are executed.
Yang et al. (Tue,) studied this question.