Journal of Scientific Computing

, Volume 61, Issue 1, pp 1–16

# 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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