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A Stabilized Galerkin Scheme for the Convection-Diffusion-Reaction Equations

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Abstract

A fully discrete stabilized scheme is proposed for solving the time-dependent convection-diffusion-reaction equations. A time derivative term results in our stabilized algorithm. The finite element method for spatial discretization and the backward Euler or Crank-Nicolson scheme for time discretization are employed. The long-time stability and convergence are established in this article. Finally, some numerical experiments are provided to confirm the theoretical analysis.

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Acknowledgements

The authors would like to thank the editor and the anonymous referees for their helpful comments and suggestions, which lead to substantial improvements of this presentation.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Qingfang Liu & Yanren Hou

  2. Center for Computational Geosciences, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Qingfang Liu & Yanren Hou

  3. School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Lei Ding

  4. School of Mechanics and Civil & Architecture, Northwestern Polytechnical University, Xi’an, 710129, P.R. China

    Qingchang Liu

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  1. Qingfang Liu
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  2. Yanren Hou
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  3. Lei Ding
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  4. Qingchang Liu
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Corresponding author

Correspondence to Yanren Hou.

Additional information

Subsidized by the Fundamental Research Funds for the Central Universities (Grant Nos. 08142013 and 08143045), NSF of China (Grant Nos. 11171269 and 11201254) and the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20110201110027).

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Liu, Q., Hou, Y., Ding, L. et al. A Stabilized Galerkin Scheme for the Convection-Diffusion-Reaction Equations. Acta Appl Math 130, 115–134 (2014). https://doi.org/10.1007/s10440-013-9840-5

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  • DOI: https://doi.org/10.1007/s10440-013-9840-5

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