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A Finite Volume Scheme with the Discrete Maximum Principle for Diffusion Equations on Polyhedral Meshes

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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

Abstract

We present a cell-centered finite volume (FV) scheme with the compact stencil formed mostly by the closest neighboring cells. The discrete solution satisfies the discrete maximum principle and approximates the exact solution with second-order accuracy. The coefficients in the FV stencil depend on the solution; therefore, the FV scheme is nonlinear. The scheme is applied to the steady state diffusion equation discretized on a general polyhedral mesh.

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Acknowledgments

This work has been supported in part by RFBR grants 12-01-33084, 14-01-00830, Russian Presidential grant MK-7159.2013.1, Federal target programs of Russian Ministry of Education and Science, ExxonMobil Upstream Research Company, and project “Breakthrough” of Rosatom.

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Authors and Affiliations

  1. Institute of Numerical Mathematics, Gubkina 8, Moscow, Russia

    Alexey Chernyshenko & Yuri Vassilevski

  2. Institute of Nuclear Safety, B.Tulskaya 52, Moscow, Russia

    Alexey Chernyshenko

  3. Moscow Institute of Physics and Technology, Institutski 9, Dolgoprudny, M.R., Russia

    Yuri Vassilevski

Authors
  1. Alexey Chernyshenko
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  2. Yuri Vassilevski
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Corresponding author

Correspondence to Alexey Chernyshenko .

Editor information

Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of Münster Center for Nonlinear Sciences (CeNoS ), Münster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

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Chernyshenko, A., Vassilevski, Y. (2014). A Finite Volume Scheme with the Discrete Maximum Principle for Diffusion Equations on Polyhedral Meshes. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_18

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