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

This work is concerned with the optimal control problems governed by a 1D wave equation with variable coefficients and the control spaces M_T of either measure-valued functions L²_w*(I, M (Ω)) or vector measures (Ω, L²(I))The cost functional involves the standard quadratic tracking terms and the regularization term α∥u∥M_T with α > 0. We construct and study three-level in time bilinear finite element discretizations for this class of problems. The main focus lies on the derivation of error estimates for the optimal state variable and the error measured in the cost functional. The analysis is mainly based on some previous results of the authors. The numerical results are included.