A simple method to generate high-order accurate convection operators for explicit schemes based on linear finite elements

A simple method is proposed to generate high-order accurate convection operators for lumped-explicit schemes based on linear or multilinear finite elements. The basic idea is to reduce the truncation error on the first-order spatial derivatives by exploiting the consistent mass matrix of the finite element method in a purely explicit multistep procedure. The effectiveness of the method is demonstrated on pure convection problems in one and two dimensions.