Convergence analysis of the Galerkin finite element method for the fourth-order Rosenau equation

Abstract

In this paper, the Galerkin finite element method (FEM) for solving the fourth-order Rosenau equation is proposed with the bicubic Hermite element. The existence and uniqueness of the approximate solution is demonstrated through the Browder fixed point theorem and the convergent result of order O(h2) in H2-norm is derived for the semi-discrete scheme. The linearized fully-discrete scheme is constructed and its error estimation of order O(h2+τ2) in H2-norm is deduced. Finally, some numerical results are provided to confirm our theoretical analysis. Here and later h and τ denote the mesh size and the time step, respectively.