, Volume 122, Issue 4, pp 645-669
Date: 14 Jul 2012

Approximation of sparse controls in semilinear equations by piecewise linear functions

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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.