Copyright © 2010 Mi Ray Ohm et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We analyze discontinuous Galerkin methods with penalty terms,
namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations.
We construct finite element spaces on which we develop fully discrete approximations using
extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection,
which leads to optimal error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.