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A Robust Residual-Type a Posteriori Error Estimator for Convection–Diffusion Equations

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Abstract

In this paper, a new robust residual type a posteriori error estimator is developed and analyzed for convection–diffusion equations. A novel dual norm is introduced, under which the error estimator is proved to be robust with respect to the singularly perturbed parameter \(\varepsilon \). Both theoretical and numerical results showed that the estimator performs better than the existing ones in literature.

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Authors and Affiliations

  1. Beijing Computational Science Research Center, No. 3 HeQing Road, Haidian District, Beijing, 100084, China

    Shaohong Du & Zhimin Zhang

  2. School of Science, Chongqing Jiaotong University, Chongqing, 400074, China

    Shaohong Du

  3. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Zhimin Zhang

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  1. Shaohong Du
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  2. Zhimin Zhang
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Correspondence to Shaohong Du.

Additional information

Shaohong Du: Research partially supported by the National Natural Science Foundation of China under Grants 91430216, 11471031 and by The Education Science Foundation of Chongqing under Grants KJ120420

Zhimin Zhang: Research partially supported by the US National Science Foundation through Grant DMS-1419040 and by the National Natural Science Foundation of China under Grants 91430216, 11471031.

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Du, S., Zhang, Z. A Robust Residual-Type a Posteriori Error Estimator for Convection–Diffusion Equations. J Sci Comput 65, 138–170 (2015). https://doi.org/10.1007/s10915-014-9972-4

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  • DOI: https://doi.org/10.1007/s10915-014-9972-4

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