  In this article we describe applications of the numerical method of discrete
differential forms in computational GR. In particular we consider the initial
value problem for vacuum space-times that admit plane gravitational waves. As
described in an earlier paper the discrete differential form approach can
provide accurate results in spherically symmetric space-times. Moreover it is
manifestly coordinate independent.
  Here we use the polarised Gowdy solution as a testbed for two numerical
schemes. One scheme reproduces that solution very well, in particular it is
stable for a comparatively long time and converges quadratically.
