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.