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Journal of Scientific Computing

, Volume 61, Issue 1, pp 1–16 | Cite as

A Robust Adaptive Grid Method for a System of Two Singularly Perturbed Convection-Diffusion Equations with Weak Coupling

  • Li-Bin Liu
  • Yanping Chen
Article

Abstract

A system of singularly perturbed convection-diffusion equations with weak coupling is considered. The system is first discretized by an upwind finite difference scheme for which an a posteriori error estimate in the maximum norm is constructed. Then the a posteriori error bound is used to design an adaptive gird algorithm. Finally, a first-order rate of convergence, independent of the perturbation parameters, is established by using the theory of the discrete Green’s function. Numerical results are presented to illustrate support our theoretical results.

Keywords

Convection-diffusion Adaptive method A posteriori error estimate  Weak coupling 

Mathematics Subject Classification (1991)

65L10 65L12 65L50 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouChina
  2. 2.Department of Mathematics and Computer ScienceChizhou CollegeChizhouChina

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