A parameter-uniform grid equidistribution method for singularly perturbed degenerate parabolic convection–diffusion problems

Abstract

We consider a class of singularly perturbed degenerate parabolic convection–diffusion problems on a rectangular domain. A numerical method is constructed using the implicit Euler scheme on a uniform mesh in the time direction and the upwind finite difference scheme on a layer adaptive non-uniform mesh in the spatial direction. The layer adaptive non-uniform mesh in the spatial direction is generated through the equidistribution of a suitably chosen monitor function. We perform error analysis through the truncation error and barrier function approach and prove that the method is uniformly convergent with first order in both time and space. Numerical results are given in support of theoretical findings.