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