We present a hybrid-mixed finite element method for a novel hybrid-dimensional model of single-phase Darcy flow in a fractured porous media. In this model, the fracture is treated as an $(d-1)$-dimensional interface within the $d$-dimensional fractured porous domain, for $d=2, 3$. Two classes of fracture are distinguished based on the permeability magnitude ratio between the fracture and its surrounding medium: when the permeability in the fracture is (significantly) larger than in its surrounding medium, it is considered as a {\it conductive} fracture; when the permeability in the fracture is (significantly) smaller than in its surrounding medium, it is considered as a {\it blocking} fracture. The conductive fractures are treated using the classical hybrid-dimensional approach of the interface model where pressure is assumed to be continuous across the fracture interfaces, while the blocking fractures are treated using the recent Dirac-$\delta$ function approach where normal component of Darcy velocity is assumed to be continuous across the interface. Due to the use of Dirac-$\delta$ function approach for the blocking fractures, our numerical scheme allows for nonconforming meshes with respect to the blocking fractures. This is the major novelty of our model and numerical discretization. Moreover, our numerical scheme produces locally conservative velocity approximations and leads to a symmetric positive definite linear system involving pressure degrees of freedom on the mesh skeleton only. The performance of the proposed method is demonstrated by various benchmark test cases in both two- and three-dimensions. Numerical results indicate that the proposed scheme is highly competitive with existing methods in the literature.

翻译：我们展示了一种混合混合的限定元素方法, 用于一种新型的单阶段达西流的混合维度模型。 在这个模型中, 骨折被视为美元( d-1) 在美元( d=2, 3美元) 的维度断裂孔域内, 美元( d=2) 3美元。 根据骨折与周围介质之间的渗透度比例, 区分了两种类型的骨折: 当骨折的渗透性( 明显) 大于周围介质, 被视为导体断裂; 当骨折的渗透性比周围介质小( 大大) 时, 断裂被视为美元( d-1) 的维度接口内, 美元( d-1 美元) 的维度界面内断裂为美元( 美元) 。 当骨折的渗透性( ) ( dirac- delta) 函数被假定为正常的导体值时, 当骨折的渗透性( ) 骨折性( Dirac- delta) 函数被使用 Dirac- dealalalalaltial) 函数方法时, 我们的直径( rodeal devial) 的直径( levelil) ) 方法被显示为正压( ) 。