The convergence of fully discrete Galerkin approximations for the Benjamin–Bona–Mahony (BBM) equation

In the present paper, we analyze a second-order in time fully discrete finite element method for the BBM equation. The discretization in space is based on the standard Galerkin method, for the time discretization the Crank–Nicolson scheme is used. We also prove the convergence of a linearized Galerkin modification scheme.