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Uniform error estimates for triangular finite element solutions of advection-diffusion equations

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Abstract

In this paper, the authors use the integral identities of triangular linear elements to prove a uniform optimal-order error estimate for the triangular element solution of two-dimensional time-dependent advection-diffusion equations. Also the authors introduce an interpolation postprocessing operator to get the superconvergence estimate under the ε weighted energy norm. The estimates above depend only on the initial and right data but not on the scaling parameter ε.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Hongtao Chen

  2. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Qun Lin

  3. School of Sciences, Hebei University of Technology, Tianjin, 300160, China

    Junming Zhou

  4. Department of Mathematics, University of South Carolina, South Carolina, 29208, USA

    Hong Wang

Authors
  1. Hongtao Chen
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  2. Qun Lin
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  3. Junming Zhou
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  4. Hong Wang
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Corresponding author

Correspondence to Hongtao Chen.

Additional information

Communicated by Reinhold Schneider.

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Chen, H., Lin, Q., Zhou, J. et al. Uniform error estimates for triangular finite element solutions of advection-diffusion equations. Adv Comput Math 38, 83–100 (2013). https://doi.org/10.1007/s10444-011-9228-x

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  • DOI: https://doi.org/10.1007/s10444-011-9228-x

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