Title: Error analysis for global minima of semilinear optimal control problems,
Abstract: In [1] we consider an optimal control problem subject to a semilinear
elliptic PDE together with its variational discretization, where we provide a
condition which allows to decide whether a solution of the necessary first
order conditions is a global minimum. This condition can be explicitly
evaluated at the discrete level. Furthermore, we prove that if the above
condition holds uniformly with respect to the discretization parameter the
sequence of discrete solutions converges to a global solution of the
corresponding limit problem. With the present work we complement our
investigations of [1] in that we prove an error estimate for those discrete
global solutions. Numerical experiments confirm our analytical findings.