A Uniform Convergence Analysis for a Bakhvalov-Type Mesh with an Explicitly Defined Transition Point
For singularly perturbed convection-diffusion problems, the truncation error and barrier-function technique for proving parameter-uniform convergence is well-known for finite-difference methods on Shishkin-type meshes (Roos and Linß in Computing, 63 (1999), 27–45). In this paper, we show that it is also possible to generalize this technique to a modification of the Bakhvalov mesh, such that the transition point between the fine and crude parts of the mesh only depends on the perturbation parameter and is defined explicitly. We provide a complete analysis for 1D problems for the simplicity of the present paper, but the analysis can be easily extended to 2D problems. With numerical results for 2D problems we show that the finite-difference discretization on the Bakhvalov-type mesh performs better than the Bakhvalov-Shishkin mesh.
Lecture Notes in Computational Science and Engineering
Vladimir A. Garanzha
Nhan, T. A. (2021). A Uniform Convergence Analysis for a Bakhvalov-Type Mesh with an Explicitly Defined Transition Point. In V. A. Garanzha, L. Kamenski, & H. Si (Eds.), Numerical Geometry, Grid Generation and Scientific Computing (pp. 213–226). Springer International Publishing. https://doi.org/10.1007/978-3-030-76798-3_13