The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders p ≥ 2

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. To cite this article: E. Burman et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).