Parameter uniform approximations for time‐dependent reaction‐diffusion problems

Using discrete Green's functions techniques, we present a classification of fitted mesh methods for time‐dependent reaction diffusion problems, based on the analyses of Linß (Linß, Numer Algor 40 (2005), 23–32) for the analogous steady‐state problem and of Kopteva (Kopteva, Computing 66 (2001), 179–197) for time‐dependent convection‐diffusion problems. As examples of how to apply the analysis, we derive error estimates for the fitted meshes of Shishkin and Bakhvalov, and provide supporting numerical results.