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This work is concerned with the optimal control problems governed by a 1Dwave equation with variable coefficients and the control spaces $\mathcal M_T$of either measure-valued functions $L_{w^*}^2(I,\mathcal M(\Omega))$ or vectormeasures $\mathcal M(\Omega,L^2(I))$. The cost functional involves the standardquadratic tracking terms and the regularization term $\alpha\|u\|_{\mathcalM_T}$ with $\alpha>0$. We construct and study three-level in time bilinearfinite element discretizations for this class of problems. The main focus lieson the derivation of error estimates for the optimal state variable and theerror measured in the cost functional. The analysis is mainly based on someprevious results of the authors. The numerical results are included.

Finite element error analysis for measure-valued optimal control problems governed by a 1D wave equation with variable coefficients