Uniformly convergent difference method for the convection-diffusion singular perturbation problem in a curved boundary region (Q1088557)

We construct a difference scheme for the convection-diffusion singular perturbation problem in a convex curved boundary region, and discuss the uniform convergence of its solution. We have proved that the order of uniform convergence of its solution is \(O(h^{\beta}+\tau^{\beta /2})\) (0 \(<\beta\) \(<\) 1/2), where h, \(\tau\) are the mesh steps in the space and time directions, respectively.