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Pointwise estimates of SDFEM on Shishkin triangular meshes for problems with characteristic layers

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Abstract

In this paper, we present pointwise estimates of the streamline diffusion finite element method (SDFEM) for conforming piecewise linears on Shishkin triangular meshes. The method is applied to a model singularly perturbed convection-diffusion problem with characteristic layers. Using a new variant of artificial crosswind diffusion, we prove that uniformly pointwise error bounds away from the layers are of order almost 7/4 (up to a logarithmic factor). In some cases, the convergence order is almost 15/8. Our analysis depends on discrete Green’s functions and sharp estimates of the diffusion and convection parts in the bilinear form. Finally, numerical experiments support our theoretical results.

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Acknowledgements

The authors thank two unknown referees for some perceptive comments that led them to improve this paper.

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Authors and Affiliations

  1. College of Science, Qilu University of Technology, Jinan, 250353, China

    Xiaowei Liu

  2. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Jin Zhang

Authors
  1. Xiaowei Liu
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  2. Jin Zhang
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Corresponding author

Correspondence to Jin Zhang.

Additional information

This research was partly supported by NSF of China (11601251), Shandong Provincial Natural Science Foundation, China (ZR2016AM13) and A Project of Shandong Province Higher Educational Science and Technology Program (J16LI10, J17KA169).

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Liu, X., Zhang, J. Pointwise estimates of SDFEM on Shishkin triangular meshes for problems with characteristic layers. Numer Algor 78, 465–483 (2018). https://doi.org/10.1007/s11075-017-0384-z

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  • DOI: https://doi.org/10.1007/s11075-017-0384-z

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