Abstract
A singularly perturbed problem with two small parameters is considered. On a Bakhvalov-type mesh we prove uniform convergence of a Galerkin finite element method with piecewise linear functions. Arguments in the error analysis include interpolation error bounds for a Clément quasi-interpolant as well as discretization error estimates in an energy norm. Numerical experiments support theoretical findings.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 307-319 |
| Number of pages | 13 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 292 |
| DOIs | |
| State | Published - Aug 3 2016 |
| Externally published | Yes |
Bibliographical note
Funding Information:The work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia , Projects 174030 and III44006 . The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which improved the quality of the paper.
Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.
Keywords
- Bakhvalov-type mesh
- Clément quasi-interpolant
- Galerkin finite element method
- Singularly perturbed problem
- Two small parameters