Galerkin finite element method for the Rosenau-RLW equation

Finite element Galerkin solutions for the Rosenau-RLW (RRLW) equation are considered. The existence and uniqueness of the weak solution are shown and the semidiscrete Galerkin scheme is studied using appropriate projections. For a second order accuracy in time, we propose the Galerkin–Crank–Nicolson fully discrete method. We also prove the convergence of the extrapolated Crank–Nicolson scheme. Finally, some numerical experiments are given to demonstrate the validity and accuracy of our method.