Fitted Numerical Methods for Singular Perturbation Problems, Revised edition, World Scientific, Singapore
- J.J.H. Miller, E. O’Riordan, G. I. Shishkin
- IMA J. Numer Anal.,
A singularly perturbed convection-diffusion problem with two small parameters is considered. The problem is solved by an upwind finite difference operator on an appropriate non-uniform mesh constructed adaptively by equi-distributing a monitor function based on the solution. An error bound in the maximum norm is established theoretically with the error constants shown to be independent of both singular perturbation parameters. The normalized flux obtained via interpolating the polynomial from the numerical solution is also uniformly convergent. A numerical experiment illustrates in practice the result of convergence proved theoretically.