Abstract
In this article, a fully discrete Galerkin scheme based on a nonlinear Crank-Nicolson method to approximate the solution of the DGRLW equation is constructed. Some a priori bounds are proved as well as error estimates. Then, a linearized modification scheme by an extrapolation method is discussed. The two schemes are time second order convergence. The last part is devoted to some numerical results. (C) 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 25: 668-684, 2009