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A mixed hybrid mortar method for solving flow in discrete fracture networks. (English) Zbl 1387.65122
Summary: We consider flow in discrete fracture networks made of 2D domains in intersection and solved with a mixed hybrid finite element method (MHFEM). The discretization within each fracture is performed in two steps: first, borders and intersections are discretized, second, based on these discretizations, a 2D mesh is built. Independent meshing process within each subdomain is of interest for practical use since it makes it easier to refine the chosen subdomains and to perform parallel computation. This article shows how MHFEM is well adapted for integrating a mortar method to enforce the continuity of the fluxes and heads at the non-matching grids. Some numerical simulations are given to show the efficiency of the method in the case of a preferential orientation of the fractures where a comparison with the 2D solution is possible.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
Full Text: DOI
[1] DOI: 10.1137/080729244 · Zbl 1387.65124 · doi:10.1137/080729244
[2] Bernardi C, in Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters pp 269– (1993)
[3] Bernardi C, in Nonlinear Partial Differential Equations and their Applications pp 13– (1994)
[4] Bernardi C, Theory and Numerics of Differential Equations pp 1– (2001)
[5] DOI: 10.1137/S0036142996308447 · Zbl 1001.65126 · doi:10.1137/S0036142996308447
[6] DOI: 10.1023/A:1019988901420 · Zbl 1079.76581 · doi:10.1023/A:1019988901420
[7] Hoteit, H.Simulation d’écoulements et de transports de polluants en milieux poreux: Application à la modélisation de la sûreté des dépôts de déchets radioactifs, PhD thesis, Rennes1 University, 2002
[8] Arnold DN, Math. Model. Numer. Anal. 19 pp 7– (1985)
[9] DOI: 10.1137/S1064827503429363 · Zbl 1083.76058 · doi:10.1137/S1064827503429363
[10] Vohralik, M.Méthodes numériques pour des équations elliptiques et paraboliques non linéaires,Application à des problèmes d’écoulement en milieux poreux et fracturés, PhD thesis, Paris IX Orsay University and Czech Technical University, Prague, 2004
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