A Galerkin finite element method that uses piecewise linear functions on Shishkin- and Bakhvalov-Shishkin-type of meshes is applied to a linear reaction-diffusion equation with discontinuous source term. The method is shown to be convergent, uniformly in the perturbation parameter, of order N-2ln2N for the Shishkin-type mesh and N-2 for the Bakhvalov-Shishkin-type mesh, where N is the mesh size number. Numerical experiments support our theoretical results.
Bibliographical noteFunding Information:
Institute of Numerical Mathematics, Technical University, D-01062 Dresden, Germany †Institute of Mathematics, Faculty of Science, University of Novi Sad, 21000 Novi Sad, Yugoslavia This paper was written during a visit to the Technical University of Dresden in June-December 2001 supported by DAAD grant.
- Finite element method
- Reaction-diffusion problems
- Shishkin mesh
- Singular perturbation