  The parallel full approximation scheme in space and time (PFASST) is a
parallel-in-time integrator that allows to integrate multiple time-steps
simultaneously. It has been shown to extend scaling limits of spatial
parallelization strategies when coupled with finite differences, spectral
discretizations, or particle methods. In this paper we show how to use PFASST
together with a finite element discretization in space. While seemingly
straightforward, the appearance of the mass matrix and the need to restrict
iterates as well as residuals in space makes this task slightly more intricate.
We derive the PFASST algorithm with mass matrices and appropriate prolongation
and restriction operators and show numerically that PFASST can, after some
initial iterations, gain two orders of accuracy per iteration.
