  In this work we consider Runge-Kutta discontinuous Galerkin methods (RKDG)
for the solution of hyperbolic equations enabling high order discretization in
space and time. We aim at an efficient implementation of DG for Euler equations
on GPUs. A mesh curvature approach is presented for the proper resolution of
the domain boundary. This approach is based on the linear elasticity equations
and enables a boundary approximation with arbitrary, high order. In order to
demonstrate the performance of the boundary curvature a massively parallel
solver on graphics processors is implemented and utilized for the solution of
the Euler equations of gas-dynamics.
