A hybrid difference scheme for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

A singularly perturbed convection diffusion problem with a discontinuous convection coefficient is considered. Due to the discontinuity an interior layer appears in the solution. The problem is solved using a hybrid difference scheme on a Shishkin mesh. We prove that the method is almost second-orde...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 169; no. 1; pp. 689 - 699
Main Author Cen, Zhongdi
Format Journal Article
LanguageEnglish
Published New York, NY Elsevier Inc 01.10.2005
Elsevier
Subjects
Convection diffusion
Exact sciences and technology
Hybrid difference scheme
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Sciences and techniques of general use
Shishkin mesh
Singularly perturbed
Convection diffusion
Shishkin mesh
Singularly perturbed
Hybrid difference scheme
Discontinuity
Discontinuous coefficient
Difference scheme
Numerical analysis
Applied mathematics
Singular perturbation
Convection diffusion equation
Diffusion coefficient
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Summary:A singularly perturbed convection diffusion problem with a discontinuous convection coefficient is considered. Due to the discontinuity an interior layer appears in the solution. The problem is solved using a hybrid difference scheme on a Shishkin mesh. We prove that the method is almost second-order convergent in the maximum norm, independently of the diffusion parameter. Numerical experiments support these theoretical results and indicate that the estimates are sharp.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2004.08.051