Numerical solution of singularly perturbed convection diffusion reaction problems with two small parameters
This paper discusses the numerical solution of linear 1 D singularly perturbed parabolic convection diffusion reaction problems with two small parameters using a moving mesh adaptive algorithm which adapts meshes to boundary layers. The meshes are generated by the equidistribution of a special positive monitor function. Parameter independent uniform convergence is shown for a class of model problems and the obtained result hold even for the limiting case where the perturbation parameters are zero. Numerical experiments are presented that illustrate the first order parameter uniform convergence, and also show that the new approach has better accuracy compared with current methods.