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

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Li-Bin Liu & Yanping Chen

  2. Department of Mathematics and Computer Science, Chizhou College, Chizhou, 247000, Anhui, China

    Li-Bin Liu

Authors
  1. Li-Bin Liu
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  2. Yanping Chen
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Corresponding author

Correspondence to Yanping Chen.

Additional information

This work is supported by National Science Foundation of China (11271145,11301044), Foundation for Talent Introduction of Guangdong Provincial University, Specialized Research Fund for the Doctoral Program of Higher Education (20114407110009), and the Project of Department of Education of Guangdong Province (2012KJCX0036), and the Scientific Research Foundation of Graduate School of South China Normal University(2012kyjj118).

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Liu, LB., Chen, Y. A Robust Adaptive Grid Method for a System of Two Singularly Perturbed Convection-Diffusion Equations with Weak Coupling. J Sci Comput 61, 1–16 (2014). https://doi.org/10.1007/s10915-013-9814-9

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  • DOI: https://doi.org/10.1007/s10915-013-9814-9

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