Sub-optimal Convergence of Non-symmetric Discontinuous Galerkin Methods for Odd Polynomial Approximations

We numerically verify that the non-symmetric interior penalty Galerkin method and the Oden-Babus̆ka-Baumann method have sub-optimal convergence properties when measured in the L-norm for odd polynomial approximations. We provide numerical examples that use piece-wise linear and cubic polynomials to approximate a second-order elliptic problem in one and two dimensions.