Explicit Multistep Mixed Finite Element Method for RLW Equation

Abstract

An explicit multistep mixed finite element method is proposed and discussed for regularized long wave (RLW) equation. The spatial direction is approximated by the mixed Galerkin method using mixed linear space finite elements, and the time direction is discretized by the explicit multistep method. The optimal error estimates in $L^2$ and $H^1$ norms for the scalar unknown $u$ and its flux $q=u_x$ based on time explicit multistep method are derived. Some numerical results are given to verify our theoretical analysis and illustrate the efficiency of our method.