  In this paper, a nonsmooth semilinear parabolic partial differential equation
(PDE) is considered. For a reduced basis (RB) approach, a space-time
formulation is used to develop a certified a-posteriori error estimator. This
error estimator is adopted to the presence of the discrete empirical
interpolation method (DEIM) as approximation technique for the nonsmoothness.
The separability of the estimated error into an RB and a DEIM part then guides
the development of an adaptive RB-DEIM algorithm, combining both offline phases
into one. Numerical experiments show the capabilities of this novel approach in
comparison with classical RB and RB-DEIM approaches.
