Energy Norm Error Estimates for Averaged Discontinuous Galerkin Methods in 1 Dimension

Abstract

Numerical solution of one-dimensional elliptic problems is investigated using an averaged discontinuous discretization. The corresponding numerical method can be performed using the favorable properties of the discontinuous Galerkin (dG) approach, while for the average an error estimation is obtained in the $H^1$-seminorm. We point out that this average can be regarded as a lower order modification of the average of a well-known overpenalized symmetric interior penalty (IP) method. This allows a natural derivation of the overpenalized IP methods.