An optimal-order error estimate for the mass-conservative characteristic finite element scheme

The mass-conservative characteristic (MCC) finite element scheme preserves the mass balance, which is an important property in the numerical simulation of the convection–diffusion problems. In this paper, an optimal-order error estimate is obtained for the model problem in one space dimension. The convergence rate is O(h2+Δt)O(h2+Δt) in the l∞(L2)l∞(L2) norm for the linear finite element. Some numerical examples are given to confirm the conclusion.