Uniform estimate for characteristics-mixed finite element method for two-dimensional advection-dominated transport problems

In this paper, we prove uniform optimal-order error estimates for characteristics-mixed finite element methods for two-dimensional convection-dominated diffusion equations. The generic constants in the error estimates do not explicitly depend on the scaling diffusion parameter epsilon, but depend linearly on certain Sobolev norms of the true solution. Combining the estimates with the stability estimates of the true solution, we prove that these constants depend only on the initial and the right-hand side data. Numerical experiments are presented to confirm our theoretical findings.