Computational issues of hybrid and multipoint mixed methods for groundwater flow in anisotropic media. (English) Zbl 1398.76104

Fontaine, Vincent; Younes, Anis

Comput. Geosci. 14, No. 1, 171-181 (2010).

Summary: 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.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76S05	Flows in porous media; filtration; seepage

Keywords:

lowest-order mixed method; Raviart-Thomas and Brezzi-Douglas-Marini finite elements; hybrid and multipoint formulations; groundwater flow

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