Abstract <p>In this work the discontinuous Galerkin method of a high order of accuracy is studied for modeling the dissipation of isotropic and homogeneous turbulence. The Navier–Stokes equations are solved on an under-resolved mesh and the LES formulation with the Smagorinsky model is also studied. The specifications for the initial conditions are varied, as is the scheme for convective fluxes. The polynomial solution within each cell allows the extended spectral resolution of the flow. It is shown that coefficient <i>C</i>_<i>S</i> of the subgrid viscosity model can be set universally despite the tested order of the scheme</p>