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.
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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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Rebelo, P.P., Palha, A., Gerritsma, M. (2014). Mixed Mimetic Spectral Element Method Applied to Darcy’s Problem. In: Azaïez, M., El Fekih, H., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012. Lecture Notes in Computational Science and Engineering, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-01601-6_30
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DOI: https://doi.org/10.1007/978-3-319-01601-6_30
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