  A novel algorithmic discussion of the methodological and numerical
differences of competing parametric model reduction techniques for nonlinear
problems are presented. First, the Galerkin reduced basis (RB) formulation is
presented which fails at providing significant gains with respect to the
computational efficiency for nonlinear problems. Renown methods for the
reduction of the computing time of nonlinear reduced order models are the
Hyper-Reduction and the (Discrete) Empirical Interpolation Method (EIM, DEIM).
An algorithmic description and a methodological comparison of both methods are
provided. The accuracy of the predictions of the hyper-reduced model and the
(D)EIM in comparison to the Galerkin RB is investigated. All three approaches
are applied to a simple uncertainty quantification of a planar nonlinear
thermal conduction problem. The results are compared to computationally intense
finite element simulations.
