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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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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DOI: https://doi.org/10.1007/978-3-319-05684-5_18
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