An almost second order parameter uniform scheme for 2D singularly perturbed boundary turning point problem

In this article, we propose to construct and analyze a higher order parameter uniform numerical scheme for a class of two dimensional (2D) parabolic singularly perturbed convection-diffusion problem with a multiple boundary turning point. The solution of the considered problem exhibits boundary layers at x = 0, y = 0 and a corner layer in the neighbourhood of (0, 0). A fractional step method on a uniform mesh is employed in time direction for semi-discretization of the problem. A hybrid scheme on a piecewise uniform mesh is used to discretize the resulting one dimensional (1D) problems in the space variables. Furthermore, Richardson extrapolation is employed in the time variable. The resulting scheme has almost second order of convergence in space direction and second order of convergence in time direction. The theoretical findings are verified through numerical experiments conducted on three test problems. Results are compared with those available in the literature to establish better accuracy and order of convergence of the proposed scheme.