Paper Info
Title
The Bakhvalov Mesh: A Complete Finite-Difference Analysis Of Two-Dimensional Singularly Perturbed Convection-Diffusion Problems
Abstract
A linear two-dimensional singularly perturbed convection-diffusion boundary-value problem is considered. The problem is discretized by the upwind finite-difference method. The analysis of this method on Shishkin-type meshes has been well-established, but the discretization mesh in this paper is the original Bakhvalov mesh, introduced in 1969 as the first layer-adapted mesh. We analyze the error of the numerical solution in the maximum norm and prove first-order pointwise accuracy, uniform in the perturbation parameter. This is the first complete analysis of this kind for two-dimensional convection-diffusion problems discretized on the Bakhvalov mesh. Our numerical experiments validate the theoretical analysis.
Year
DOI
Venue
2021
10.1007/s11075-020-00964-z
NUMERICAL ALGORITHMS
Keywords
DocType
Volume
Singular perturbation, Convection-diffusion, Bakhvalov mesh, Finite differences, Uniform convergence
Journal
87
Issue
ISSN
Citations 
1
1017-1398
1
PageRank 
References 
Authors
0.39
0
2
Name
Order
Citations
PageRank
Thái Anh Nhan110.39
Relja Vulanovic23513.39