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 OJAppS  Vol.2 No.4 B , December 2012
The uniform convergence of upwind schemes on layer-adapted meshes for a singularly perturbed Robin BVP
Quan Zheng*, Fengxi Huang, Xiaoli Feng, Mengbin Han
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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
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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