In this paper, a conservative finite volume element scheme for solving the regularized long wave equation is presented. Theoretical analysis shows that the proposed scheme can conserve the mass and energy. The efficiency of the scheme is illustrated by simulating propagation of single solitary wave, interaction of two solitary waves and undular bores. Numerical results indicate that this scheme is second-order accuracy in space and time, and has good conservation properties.
Mathematics Subject Classification: 65N12; 76D07
Keywords: conservative; RLW equation; finite volume element