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Analysis of SDFEM on Shishkin Triangular Meshes and Hybrid Meshes for Problems with Characteristic Layers

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Abstract

In this paper, we analyze the streamline diffusion finite element method (SDFEM) for a model singularly perturbed convection–diffusion equation on a Shishkin triangular mesh and hybrid meshes. Supercloseness property of \(u^I-u^N\) is obtained, where \(u^I\) is the interpolant of the solution u and \(u^N\) is the SDFEM’s solution. The analysis depends on novel integral inequalities for the diffusion and convection parts in the bilinear form. Furthermore, analysis on hybrid meshes shows that bilinear elements should be recommended for the exponential layer, not for the characteristic layer. 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

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

Additional information

This research was partly supported by NSF of China (Grant Nos. 11501335, 11401349 and 11501334) and NSF of Shandong Province (Grant Nos. BS2014SF008 and ZR2015FQ014).

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Zhang, J., Liu, X. Analysis of SDFEM on Shishkin Triangular Meshes and Hybrid Meshes for Problems with Characteristic Layers. J Sci Comput 68, 1299–1316 (2016). https://doi.org/10.1007/s10915-016-0180-2

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  • DOI: https://doi.org/10.1007/s10915-016-0180-2

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