A second-order scheme for singularly perturbed differential equations with discontinuous source term

H. G. Roos; H. Zarin

doi:10.1515/JNMA.2002.275

A second-order scheme for singularly perturbed differential equations with discontinuous source term

H. G. Roos, H. Zarin

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	275-289
Number of pages	15
Journal	Journal of Numerical Mathematics
Volume	10
Issue number	4
DOIs	https://doi.org/10.1515/JNMA.2002.275
State	Published - 2002
Externally published	Yes

Bibliographical note

Funding 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.

Keywords

Finite element method
Reaction-diffusion problems
Shishkin mesh
Singular perturbation

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AU - Zarin, H.

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N2 - 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.

AB - 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.

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KW - Reaction-diffusion problems

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KW - Singular perturbation

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A second-order scheme for singularly perturbed differential equations with discontinuous source term

Abstract

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Keywords

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