Approximation of sparse controls in semilinear equations by piecewise linear functions - Casas, Eduardo; Herzog, Roland; Wachsmuth, Gerd (Numerische Mathematik, 2012)
Semilinear elliptic optimal control problems involving the 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.