A note on a generalized Shishkin-type mesh

Authors

Thái Ahn Nhan, Santa Clara UniversityFollow
Relja Vulanović

Document Type

Article

Publication Date

2018

Publisher

Department of Mathematics and Informatics,Faculty of Sciences,University of Novi Sad, Serbia

Abstract

The one-dimensional linear singularly perturbed convection-diffusion problem is discretized using the upwind scheme on a mesh which is a mild generalization of Shishkin-type meshes. The generalized mesh uses the transition point of the Shishkin mesh, but it does not require any structure of its fine and course parts. Convergence uniform in the perturbation parameter is proved by the barrier-function technique, which, because of the unstructured mesh, does not rely on any mesh-generating function. In this way, the technical requirements needed in the existing barrier-function approaches are simplified.

Comments

All articles published in our journal are open access and freely available online, immediately upon publication, and used under the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence

Recommended Citation

Nhan, T. A., & Vulanović, R. (2018). A note on a generalized Shishkin-type mesh. Novi Sad Journal of Mathematics, 48(2), 141–150. https://doi.org/10.30755/NSJOM.07880