Author(s)

Quan Zheng, Fengxi Huang, Xiaoli Feng, Mengbin Han

College of Sciences, North China University of Technology, Beijing 100144, China.

In this paper, we discuss the uniform convergence of the simple upwind scheme on the Shishkin mesh and the Bakhvalov-Shishkin mesh for solving a singularly perturbed Robin boundary value problem, and investigate the midpoint upwind scheme on the Shishkin mesh and the Bakhvalov-Shishkin mesh to achieve better uniform convergence. The elaborate ε-uniform pointwise estimates are proved by using the comparison principle and barrier functions. The numerical experiments support the theoretical results for the schemes on the meshes.

Singularly perturbed Robin BVP; simple upwind scheme; midpoint upwind scheme; layer-adapted mesh; uniform convergence

Zheng, Q. , Huang, F. , Feng, X. and Han, M. (2012) The uniform convergence of upwind schemes on layer-adapted meshes for a singularly perturbed Robin BVP. Open Journal of Applied Sciences, 2, 66-69. doi: 10.4236/ojapps.2012.24B016.