The lowest order characteristic mixed finite element scheme for convection-dominated diffusion problem

A new characteristic mixed finite element method (MFEM) is proposed by combining the method of characteristics with the new mixed variational formulation for the convection-dominated diffusion problem. The error estimates for both the original variable uu and auxiliary variable p→ are derived via the properties of the integral identity and mean value techniques. At the same time, some numerical experiments are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.