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An adaptive strategy for solving convection dominated diffusion equation

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Abstract

In this work, an adaptive element free Galerkin (EFG) technique is proposed for solving convection diffusion equation. A post-processed gradient is used as a posteriori error estimation to find locations with large contribution of the error. Also, to avoid instabilities, the EFG method is applied on a modified equation instead of the original equation. In the modified equation diffusion coefficient (known as artificial diffusion) depends to the distance between nodal points. The numerical results reveal efficiency of the adaptive technique.

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Acknowledgements

The authors are very grateful to reviewers for carefully reading the paper and for their constructive comments and suggestions. This research was in part supported by a grant from IPM (No. 95650422).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Zahra Jannesari & Mehdi Tatari

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran

    Mehdi Tatari

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  1. Zahra Jannesari
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  2. Mehdi Tatari
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Correspondence to Mehdi Tatari.

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Communicated by Corina Giurgea.

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Jannesari, Z., Tatari, M. An adaptive strategy for solving convection dominated diffusion equation. Comp. Appl. Math. 39, 78 (2020). https://doi.org/10.1007/s40314-020-1081-4

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  • DOI: https://doi.org/10.1007/s40314-020-1081-4

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