Analysis and simulation of Korteweg-de Vries-Rosenau-regularised long-wave model via Galerkin finite element method

In this paper, a Galerkin finite element method is designed and analyzed to simulate the nonlinear Korteweg-de Vries-Rosenau-regularized long-wave (KdV-RRLW) model. We establish the existence and uniqueness results in H02(Ω) Sobolev space by applying the Banach–Alaoglu theorem. Using appropriate projection, we derive the error estimates of a semidiscrete scheme for the finite element solution of the KdV-RRLW model. Furthermore, a second-order Crank-Nicolson scheme is employed for the temporal discretization and obtain the optimal order of convergence in the maximum norm. Finally, several numerical examples are provided to visualize the nature of the wave phenomena in one and two dimensional spaces and demonstrate the robustness of the developed finite element algorithm.