We propose a hybridized domain decomposition formulation of the discrete fracture network model, allowing for independent discretization of the individual fractures. A natural norm stabilization, obtained by penalizing the residual measured in the norm for the space where it naturally lives, is added to the local problem in the individual fracture so that no compatibility condition of inf-sup type is required between the Lagrange multiplier and the primal unknown, which can then be discretized independently of each other. Optimal stability and error estimates are proven, which are confirmed by numerical tests.

翻译：本文提出了一种离散裂缝网络模型的混合域分解变分格式，允许对各独立裂缝进行独立的离散化。通过在局部裂缝问题中引入一种自然范数稳定化方法——即对残差在其自然所属空间范数下的度量进行惩罚，该格式无需在拉格朗日乘子与原始未知量之间满足 inf-sup 类型的兼容性条件，从而可实现二者的独立离散。我们证明了该格式具有最优的稳定性和误差估计，并通过数值实验验证了理论结果。