TITLE:
The uniform convergence of upwind schemes on layer-adapted meshes for a singularly perturbed Robin BVP
AUTHORS:
Quan Zheng, Fengxi Huang, Xiaoli Feng, Mengbin Han
KEYWORDS:
Singularly perturbed Robin BVP; simple upwind scheme; midpoint upwind scheme; layer-adapted mesh; uniform convergence
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.2 No.4B,
January
11,
2013
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.