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Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers

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Abstract

In this paper, we analyze the supercloseness property of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes, which is different from one in the case of rectangular meshes. The analysis depends on integral inequalities for the parts related to the diffusion in the bilinear form. Moreover, our result allows the construction of a simple postprocessing that yields a more accurate solution. Finally, numerical experiments support these theoretical results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China

    Jin Zhang

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

    Xiaowei Liu

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  1. Jin Zhang
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  2. Xiaowei Liu
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Correspondence to Jin Zhang.

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Communicated by: Jinchao Xu

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Zhang, J., Liu, X. Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers. Adv Comput Math 43, 759–775 (2017). https://doi.org/10.1007/s10444-016-9505-9

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  • DOI: https://doi.org/10.1007/s10444-016-9505-9

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