Energy-preserving finite volume element method for the improved Boussinesq equation

In this paper, we design an energy-preserving finite volume element scheme for solving the initial boundary problems of the improved Boussinesq equation. Theoretical analysis shows that the proposed numerical schemes can conserve the energy and mass. Numerical experiments are performed to illustrate the efficiency of the scheme and theoretical analysis. While the results demonstrate that the proposed finite volume element scheme is second-order accuracy in space and time. Moreover, the new scheme can conserve mass and energy.