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A Family of Fourth-Order and Sixth-Order Compact Difference Schemes for the Three-Dimensional Poisson Equation

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Abstract

In this paper a family of fourth-order and sixth-order compact difference schemes for the three dimensional (3D) linear Poisson equation are derived in detail. By using finite volume (FV) method for derivation, the highest-order compact schemes based on two different types of dual partitions are obtained. Moreover, a new fourth-order compact scheme is gained and numerical experiments show the new scheme is much better than other known fourth-order schemes. The outline for the nonlinear problems are also given. Numerical experiments are conducted to verify the feasibility of this new method and the high accuracy of these fourth-order and sixth-order compact difference scheme.

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Acknowledgements

The authors are very thankful to the anonymous referee who meticulously read through the paper, made many helpful discussions and corrections of the English and typesetting mistakes. The second author gratefully acknowledge the financial support from Hong Kong Scholars Program. This work is in part supported by the NSF of China (Nos. 61163027, 10971166, 10901131), the National High Technology Research and Development Program of China (863 Program, No. 2009AA01A135), the China Postdoctoral Science Foundation (Nos. 201104702, 2012M512056), the Key Project of Chinese Ministry of Education (No. 212197), the NSF of Xinjiang Province (No. 2010211B04) and the Excellent Doctor Innovation Program of Xinjiang University.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, China

    Shuying Zhai, Xinlong Feng & Yinnian He

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Xinlong Feng

  3. Center for Computational Geosciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Yinnian He

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  1. Shuying Zhai
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Correspondence to Xinlong Feng.

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Zhai, S., Feng, X. & He, Y. A Family of Fourth-Order and Sixth-Order Compact Difference Schemes for the Three-Dimensional Poisson Equation. J Sci Comput 54, 97–120 (2013). https://doi.org/10.1007/s10915-012-9607-6

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  • DOI: https://doi.org/10.1007/s10915-012-9607-6

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