  One popular approach to option pricing in L\'evy models is through solving
the related partial integro differential equation (PIDE). For the numerical
solution of such equations powerful Galerkin methods have been put forward e.g.
by Hilber et al. (2013). As in practice large classes of models are maintained
simultaneously, flexibility in the driving L\'evy model is crucial for the
implementation of these powerful tools. In this article we provide such a
flexible finite element Galerkin method. To this end we exploit the Fourier
representation of the infinitesimal generator, i.e. the related symbol, which
is explicitly available for the most relevant L\'evy models. Empirical studies
for the Merton, NIG and CGMY model confirm the numerical feasibility of the
method.
