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A High-Order Upwind Method for Convection-Diffusion Equations with the Newmann Boundary Condition

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Book cover Numerical Treatment of Multiphase Flows in Porous Media

Part of the book series: Lecture Notes in Physics ((LNP,volume 552))

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Abstract

In this paper a high-order upwind finite difference method is studied for steady convection-diffusion problems with the Newmann boundary condition. Based on these equations in the conservation form, a conservative high-order upwind finite difference scheme on nonuniform rectangular partition is proposed. The scheme satisfies the maximum value principle and has a second-order error estimate in the discrete H 1 norm. The method and its analysis apply to groundwater pollution and reservoir simulation problems.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Shandong University, Jinan, P. R. China

    Weidong Zhao

Authors
  1. Weidong Zhao
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Southern Methodist University, Box 750156, 75275-0156, Dallas, TX, USA

    Zhangxin Chen

  2. Institute for Scientific Computation, Texas A&M University, 77843-3404, College Station, TX, USA

    Richard E. Ewing

  3. Institute of ComputaTional Mathematics, Chinese Academy of Sciences, P.O.Box 2719, 100080, Beijing, P.R.China

    Zhong-Ci Shi

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© 2000 Springer-Verlag Berlin Heidelberg

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Zhao, W. (2000). A High-Order Upwind Method for Convection-Diffusion Equations with the Newmann Boundary Condition. In: Chen, Z., Ewing, R.E., Shi, ZC. (eds) Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics, vol 552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45467-5_38

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  • DOI: https://doi.org/10.1007/3-540-45467-5_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67566-2

  • Online ISBN: 978-3-540-45467-0

  • eBook Packages: Springer Book Archive

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