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Arbitrary order nodal mimetic discretizations of elliptic problems on polygonal meshes

  • Lourenço Beirão da VeigaEmail author
  • Konstantin Lipnikov
  • Gianmarco Manzini
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)

Abstract

We develop and analyze a new family of mimetic methods on unstructured polygonal meshes for the diffusion problem in primal form. The new nodal formulation that we propose in this work extends the original low-order formulation of [3] to arbitrary orders of accuracy by requiring that the consistency condition holds for polynomials of arbitrary degree m ≥ 1. An error estimate is presented in a mesh-dependent norm that mimics the energy norm and numerical experiments confirm the convergence rate that is expected from the theory.

Keywords

mimetic finite difference diffusion problems unstructured mesh polygonal element 

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Notes

Acknowledgements

The work of the second author was supported by the Department of Energy (DOE) Advanced Scientific Computing Research (ASCR) program in Applied Mathematics. The work of the third author was partially supported by the Italian MIUR through the program PRIN2008.

References

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    F. Brezzi, K. Lipnikov, and M. Shashkov. Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes. SIAM J. Numer. Anal., 43(5):1872–1896, 2005.MathSciNetzbMATHCrossRefGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Lourenço Beirão da Veiga
    • 1
    Email author
  • Konstantin Lipnikov
    • 2
  • Gianmarco Manzini
    • 3
  1. 1.Dipartimento di MatematicaUniversità di MilanoMilanoItaly
  2. 2.Los Alamos National LaboratoryNew MexicoUS
  3. 3.IMATI-CNR and CeSNA-IUSSPaviaItaly

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