A numerical approximation of a convection–reaction–diffusion problem by standard bilinear finite elements is considered. Using Duran–Lombardi and Duran–Shishkin type meshes we prove first order error estimates in an energy norm. Numerical examples confirm our theoretical results and show smaller errors compared to the well-known Shishkin mesh.
Bibliographical noteFunding Information:
The work was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia , Projects III44006 and 174030 .
© 2016 Elsevier Ltd
- Galerkin finite element method
- Graded meshes
- Singularly perturbed problem
- Two small parameters