Uniform estimates for characteristics-mixed finite method for transient advection-dominated diffusion problems in two-dimensional space

• We prove uniform optimal-order error estimates for the characteristics-mixed finite element for advection–diffusion equations.
• In the proof, the interpolation operators are used instead of the mixed elliptic projections.
• The generic constants of the estimates do not explicitly depend on ε, but depend linearly on Sobolev norms of the true solution.

We prove uniform error estimates for the characteristics-mixed finite element method for two-dimensional transient convection-dominated diffusion equations, in the sense that the generic constants in the error estimates depend linearly on certain Sobolev norms of the true solution but not on the scaling diffusion parameter ε. Numerical experiments are presented to confirm our theoretical findings.