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

Burman, ErikErn, AlexandreMozolevski, IgorStamm, Benjamin2007-10-052007-10-052007-10-05200710.1016/j.crma.2007.10.028https://infoscience.epfl.ch/handle/20.500.14299/12705WOS:00025223250001111751In this Note we prove that in one space dimension, the symmetric discontinuous Galerkin method for second order elliptic problems is stable for polynomial orders $p \ge 2$ without using any stabilization parameter. The method yields optimal convergence rates in both the broken energy norm and the $L^2$- norm and can be written in conservative form with fluxes independent of any stabilization parameter.The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders p ≥ 2text::journal::journal article::research article