These past few years, new types of computational architectures based on graphics processors have emerged. These technologies provide important computational resources at low cost and low energy consumption. Lots of developments have been done around GPU and many tools and libraries are now available to implement efficiently softwares on those architectures. This article contains the two contributions of the mini-symposium about GPU organized by Loïc Gouarin (Laboratoire de Mathématiques d’Orsay), Alexis Hérault (CNAM) and Violaine Louvet (Institut Camille Jordan). This mini-symposium was an opportunity to explore the upcoming role of hardware accelerators and how it will affect the way applications are designed and developed. As the main issue of the mini-symposium was graphical cards, this document contains contributions about two feedbacks on the behavior of different numerical methods on GPU: ones on particle method for transport equations, the other on Lattice Boltzmann Methods for Navier–Stokes equations, Finite Volume schemes for Euler equations and particles methods for kinetic equations.