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. © 2013 Elsevier Ltd. All rights reserved.
Atouani, N., & Omrani, K. (2013). Galerkin finite element method for the Rosenau-RLW equation. Computers and Mathematics with Applications, 66(3), 289–303. https://doi.org/10.1016/j.camwa.2013.04.029