Abstract
In this work, we review a set of consistent discretizations for second-order elliptic equations, and compare and contrast them with respect to accuracy, monotonicity, and factors affecting their computational cost (degrees of freedom, sparsity, and condition numbers). Our comparisons include the linear and nonlinear TPFA method, multipoint flux-approximation (MPFA-O), mimetic methods, and virtual element methods. We focus on incompressible flow and study the effects of deformed cell geometries and anisotropic permeability.
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Notes
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Other choices of primary pressure points are also possible, e.g., circumcenter for triangular grids.
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Acknowledgements
Klemetsdal, Lie, and Raynaud were supported by the Research Council of Norway (244361). Møyner is funded by VISTA, a basic research programme funded by Equinor and conducted in close collaboration with The Norwegian Academy of Science and Letters.
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Klemetsdal, Ø.S., Møyner, O., Raynaud, X., Lie, KA. (2020). A Comparison of Consistent Discretizations for Elliptic Problems on Polyhedral Grids. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_55
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