A Uniformly Convergent Numerical Algorithm on Harmonic (H(l)) Mesh for Parabolic Singularly Perturbed Convection-Diffusion Problems with Boundary Layer

This paper deals the design and analysis of a parameter uniform finite difference algorithm for a class of parabolic singularly perturbed convection-diffusion problems. The discrete nearby problem is designed using the backward Euler scheme in time and upwind scheme on H(l) mesh in space. We present the convergence analysis of the algorithm, which proves that it is parameter uniform in L-infinity norm. The numerical experiments support the theoretical estimates and demonstrates the efficiency of H(l) mesh with the existing meshes, like Shishkin and Bakhvalov type meshes.