The uniform convergence of upwind schemes on layer-adapted meshes for a singularly perturbed Robin BVP

Quan Zheng, Fengxi Huang, Xiaoli Feng, Mengbin Han

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

DOI: 10.4236/ojapps.2012.24B016                

Abstract

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

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