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.
Cite this paper
nullZheng, 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.
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