We present a two-dimensional Cartesian code based on high-order discontinuous Galerkin methods, implemented to run in parallel over multiple graphics processing units. A simple planet–disc setup is used to compare the behaviour of our code against the behaviour found using the FARGO3D code with a polar mesh. We make use of the time dependence of the torque exerted by the disc on the planet as a mean to quantify the numerical viscosity of the code. We find that the numerical viscosity of the Keplerian flow can be as low as a few 10−8r2Ω, r and Ω being respectively the local orbital radius and frequency, for fifth-order schemes and resolution of ∼10−2r. Although for a single disc problem a solution of low numerical viscosity can be obtained at lower computational cost with FARGO3D (which is nearly an order of magnitude faster than a fifth-order method), discontinuous Galerkin methods appear promising to obtain solutions of low numerical viscosity in more complex situations where the flow cannot be captured on a polar or spherical mesh concentric with the disc.