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.
Bibliographical noteFunding 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.
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- Bakhvalov-type mesh
- Clément quasi-interpolant
- Galerkin finite element method
- Singularly perturbed problem
- Two small parameters