Galerkin finite element method for the Rosenau-RLW equation

摘要

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.