Finite element galerkin solutions for the rosenau equation

Abstract

Finite element Galerkin approximate solutions for a KdV–like Rosenau equation which models the dynamics of dense discrete systems are considered. Existence and uniqueness of exact solutions are shown and the error estimates of the continuous time Galerkin solutions are discussed. For the fully discrete time Galerkin solutions, we consider the backward Euler method which results the first order convergence in the temporal direction. For the second order convergence in time, we consider a three–level backward method and the Crank–Nicolson method which give optimal convergence in the spatial direction.