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

  • Alexey ChernyshenkoEmail author
  • Yuri Vassilevski
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 77)


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.


Diffusive Flux Collocation Point Numerical Flux Finite Volume Scheme Discrete Maximum Principle 
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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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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institute of Numerical MathematicsMoscowRussia
  2. 2.Institute of Nuclear SafetyMoscowRussia
  3. 3.Moscow Institute of Physics and TechnologyDolgoprudny, M.R.Russia

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