  This paper is concerned with error estimates for the numerical approximation
for affine optimal control problems subject to semilinear elliptic PDEs. To
investigate the error estimates, we focus on local minimizers that satisfy
certain local growth conditions. The local growth conditions we consider in
this paper appeared recently in the context of solution stability and contain
the joint growth of the first and second variation of the objective functional.
These growth conditions are especially meaningful for affine control
constrained optimal control problems because the first variation can satisfy a
local growth, which is not the case for unconstrained problems. The main
results of this paper are the achievement of error estimates for the numerical
approximations generated by a finite element scheme with piecewise constant
controls or a variational discretization scheme. Even though the growth
conditions considered are weaker than those appearing in the recent literature
on finite element error estimates for affine problems, this paper substantially
improves the existing error estimates for both the optimal controls and the
states when a H\"older-type growth is assumed.
