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Nodal Superconvergence of SDFEM for Singularly Perturbed Problems

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Abstract

In this paper, we analyze the streamline diffusion finite element method for one dimensional singularly perturbed convection-diffusion-reaction problems. Local error estimates on a subdomain where the solution is smooth are established. We prove that for a special group of exact solutions, the nodal error converges at a superconvergence rate of order (ln ε −1/N)2k (or (ln N/N)2k) on a Shishkin mesh. Here ε is the singular perturbation parameter and 2N denotes the number of mesh elements. Numerical results illustrating the sharpness of our theoretical findings are displayed.

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Authors and Affiliations

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

    Fatih Celiker & Zhimin Zhang

  2. Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS, 39406, USA

    Huiqing Zhu

Authors
  1. Fatih Celiker
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  2. Zhimin Zhang
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  3. Huiqing Zhu
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Correspondence to Huiqing Zhu.

Additional information

Part of this work was done when the first author was a long-term visitor at the Institute for Mathematics and its Applications (IMA), University of Minnesota, MN, during the Fall semester of 2010.

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Celiker, F., Zhang, Z. & Zhu, H. Nodal Superconvergence of SDFEM for Singularly Perturbed Problems. J Sci Comput 50, 405–433 (2012). https://doi.org/10.1007/s10915-011-9489-z

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  • DOI: https://doi.org/10.1007/s10915-011-9489-z

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