Singularly Perturbed System of Parabolic PDE: A Numerical Apprach

We have studied numerical scheme for the singularly perturbed system of parabolic convection-diffusion problems with boundary and interior layers on an adaptive piecewise uniform mesh. Due to the boundary layer behavior of the exact solution, it is interesting and the same time quite difficult to develop robust computation techniques for the model problem of multi-scale nature. To improve the accuracy (form almost first-order to second-order), the hybrid difference scheme and extrapolation technique has been used. Later, we have examined the fractional step method for the system of 2D parabolic reaction-diffusion and convection-diffusion problems with overlapping boundary layers. We have established a priori error analysis of the discrete problem and produce numerical results which confirm the theoretical finding.