Robust numerical scheme for singularly perturbed convection-diffusion parabolic initial-boundary-value problems on equidistributed grids

In this article, we study the numerical solution of singularly perturbed parabolic convection-diffusion problems exhibiting regular boundary layers. To solve these problems, we use the classical upwind finite difference scheme on layer-adapted nonuniform meshes. The nonuniform meshes are obtained by equidistributing a positive monitor function, which depends on the second-order spatial derivative of the singular component of the solution. The truncation error and the stability analysis are obtained. Parameter-uniform error estimates are derived for the numerical solution. Semilinear IBVPs are also solved. Numerical experiments are carried out to support the theoretical results.