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Mixed Mimetic Spectral Element Method Applied to Darcy’s Problem

  • Pedro Pinto Rebelo
  • Artur Palha
  • Marc Gerritsma
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 95)

Abstract

We present a discretization for Darcy’s problem using the recently developed Mimetic Spectral Element Method (Kreeft et al. (2011) Mimetic framework on curvilinear quadrilaterals of arbitrary order. Submitted to FoCM, Arxiv preprint arXiv:1111.4304). The gist lies in the exact discrete representation of integral relations. In this paper, an anisotropic flow through a porous medium is considered and a discretization of a full permeability tensor is presented. The performance of the method is evaluated on standard test problems, converging at the same rate as the best possible approximation.

Keywords

Edge Function Saddle Point Problem Spectral Element Method Anisotropic Permeability Positive Definite Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors gratefully acknowledge the funding received by FCT – Foundation for science and technology Portugal through SRF/BD/36093/2007 and SFRH/BD/79866/2011 and the anonymous reviewers for their helpful comments.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Pedro Pinto Rebelo
    • 1
  • Artur Palha
    • 1
  • Marc Gerritsma
    • 1
  1. 1.Faculty of Aerospace Engineering, Aerodynamics GroupDelft University of TechnologyDelftThe Netherlands

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