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Mimetic Finite Difference Schemes with Conditional Maximum Principle for Diffusion Problems

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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))

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Abstract

Numerical schemes that satisfy the maximum principle play important role in multiphysics codes. They reduce significantly various numerical artifacts. We describe a novel inexpensive practical algorithm for building mimetic finite difference schemes with conditional maximum principle on polygonal and polyhedral meshes for diffusion problems.

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References

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Acknowledgments

This work was performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. The author gratefully acknowledges the partial support of the US Department of Energy Office of Science Advanced Scientific Computing Research (ASCR) Program in Applied Mathematics Research and Office of Environmental Management Advanced Simulation Capability for Environmental Management (ASCEM) Program.

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Authors and Affiliations

  1. Los Alamos National Laboratory, Los Alamos, NM, 87544, USA

    Konstantin Lipnikov

Authors
  1. Konstantin Lipnikov
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Correspondence to Konstantin Lipnikov .

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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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Lipnikov, K. (2014). Mimetic Finite Difference Schemes with Conditional Maximum Principle for Diffusion Problems. 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_36

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