  This paper introduces the FEDM (Finite Element Discharge Modelling) code,
which was developed using the open-source computing platform FEniCS
(https://fenicsproject.org). Building on FEniCS, the FEDM code utilises the
finite element method to solve partial differential equations. It extends
FEniCS with features that allow the automated implementation and numerical
solution of fully-coupled fluid-Poisson models including an arbitrary number of
particle balance equations. The code is verified using the method of exact
solutions and benchmarking. The physically based examples of a time-of-flight
experiment, a positive streamer discharge in atmospheric-pressure air and a
low-pressure glow discharge in argon are used as rigorous test cases for the
developed modelling code and to illustrate its capabilities. The performance of
the code is compared to the commercial software package COMSOL
Multiphysics\textsuperscript{\textregistered} and a comparable parallel
speed-up is obtained. It is shown that the iterative solver implemented by FEDM
performs particularly well on high-performance compute clusters.
