The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders
Résumé
In this Note we prove that in one space dimension, the symmetric discontinuous Galerkin method for second order elliptic problems is stable for polynomial orders p⩾2 without using any stabilization parameter. The method yields optimal convergence rates in both the energy norm (L2-norm of broken gradient plus jump terms) and the L2-norm and can be written in conservative form with fluxes independent of any stabilization parameter.