Approximation of sparse controls in semilinear equations by piecewise linear functions
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- Casas, E., Herzog, R. & Wachsmuth, G. Numer. Math. (2012) 122: 645. doi:10.1007/s00211-012-0475-7
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Semilinear elliptic optimal control problems involving the \(L^1\) norm of the control in the objective are considered. A priori finite element error estimates for piecewise linear discretizations for the control and the state are proved. These are obtained by a new technique based on an appropriate discretization of the objective function. Numerical experiments confirm the convergence rates.