An adaptive mesh strategy for singularly perturbed convection diffusion problems

In this paper, a new adaptive mesh strategy has been developed for solving convection dominated, convection-diffusion singularly perturbed problems (SPP) using second order central difference schemes. Our strategy uses a novel, entropy-like variable as the adaptation parameter for convection diffusion SPP. Further, unlike the popular layer adapted meshes mainly by Bakhvalov (B-type) and Shishkin (S-type), no pre-knowledge of the location and width of the layers (boundary as well as interior) is needed. The method is completely free of arbitrary perturbation parameters ∊ (robust) and results in oscillation free solutions to a range of convection-diffusion SPP. Numerical results for various test problems: linear (boundary layers with and without turning points), nonlinear and systems of coupled equations are presented. This method is expected to aid in robust computations of convection dominated SPP.