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Computational issues of hybrid and multipoint mixed methods for groundwater flow in anisotropic media

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Abstract

In this work, lowest-order Raviart–Thomas and Brezzi–Douglas–Marini mixed methods are considered for groundwater flow simulations. Typically, mixed methods lead to a saddle-point problem, which is expensive to solve. Two approaches are numerically compared here to allow an explicit velocity elimination: (1) the well-known hybrid formulation leading to a symmetric positive definite system where the only unknowns are the Lagrange multipliers and (2) a more recent approach, inspired from the multipoint flux approximation method, reducing low-order mixed methods to cell-centered finite difference schemes. Selected groundwater flow scenarios are used for the comparison between hybrid and multipoint approaches. The simulations are performed in the bidimensional case with a general triangular discretization because of its practical interest for hydrogeologists.

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Authors and Affiliations

  1. LPBS, Department of Physics, University of La Réunion, 15 avenue René Cassin, 97715, La Réunion, France

    Vincent Fontaine

  2. LHyGeS, University of Strasbourg/EOST, 1 rue Blessig, 67084, Strasbourg, France

    Anis Younes

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  1. Vincent Fontaine
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  2. Anis Younes
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Correspondence to Vincent Fontaine.

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Fontaine, V., Younes, A. Computational issues of hybrid and multipoint mixed methods for groundwater flow in anisotropic media. Comput Geosci 14, 171–181 (2010). https://doi.org/10.1007/s10596-009-9141-2

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  • DOI: https://doi.org/10.1007/s10596-009-9141-2

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