  This work is concerned with optimal control problems where the objective
functional consists of a tracking-type functional and an additional "multibang"
regularization functional that promotes optimal control taking values from a
given discrete set pointwise almost everywhere. Under a regularity condition on
the set where these discrete values are attained, error estimates for the
Moreau--Yosida approximation (which allows its solution by a semismooth Newton
method) and the discretization of the problem are derived. Numerical results
support the theoretical findings.
