  We consider the Navier-Stokes equations in a channel with a narrowing of
varying height. The model is discretized with high-order spectral element
ansatz functions, resulting in 6372 degrees of freedom. The steady-state
snapshot solutions define a reduced order space through a standard POD
procedure. The reduced order space allows to accurately and efficiently
evaluate the steady-state solutions for different geometries. In particular, we
detail different aspects of implementing the reduced order model in combination
with a spectral element discretization. It is shown that an expansion in
element-wise local degrees of freedom can be combined with a reduced order
modelling approach to enhance computational times in parametric many-query
scenarios.
