TY - GEN A1 - Casas, Eduardo A1 - Herzog, Roland A1 - Wachsmuth, Gerd T1 - Optimality Conditions and Error Analysis of Semilinear Elliptic Control Problems with L¹ Cost Functional T2 - SIAM Journal on Optimization N2 - Semilinear elliptic optimal control problems involving the L¹ norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise linear discretizations of the state are shown. Error estimates for the variational discretization of the problem in the sense of [M. Hinze, Comput. Optim. Appl., 30 (2005), pp. 45–61] are also obtained. Numerical experiments confirm the convergence rates. KW - optimal control of partial differential equations KW - nondifferentiable objective KW - sparse controls KW - finite element discretization KW - a priori error estimates Y1 - 2012 U6 - https://doi.org/10.1137/110834366 SN - 1052-6234 SN - 1095-7189 VL - 22 IS - 3 SP - 795 EP - 820 ER -