We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion. Starting from a common background bulk mesh, that covers the domain, finite element spaces are constructed for the interface and bulk subdomains leading to efficient computations of the coupling terms. The crack pressure field also uses the bulk mesh for its representation. The interface conditions are a generalized form of conditions of Robin type previously considered in the literature which allows the modeling of a range of flow regimes across the fracture. The method is robust in the following way: 1. Stability of the formulation in the full range of parameter choices; and 2. Not sensitive to the location of the interface in the background mesh. We derive an optimal order a priori error estimate and present illustrating numerical examples.

中文翻译：

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裂隙介质压力模型的切割有限元方法

我们为裂隙介质中的扩散模型开发了一种稳健的切割有限元方法，该模型由带有嵌入裂纹的体域组成。裂缝有自己的压力场，可以以非常普遍的方式穿过大块网格。从覆盖域的公共背景体网格开始，为界面和体子域构造有限元空间，从而有效计算耦合项。裂纹压力场也使用体网格来表示。界面条件是先前在文献中考虑的 Robin 类型条件的一般形式，它允许对穿过裂缝的一系列流态进行建模。该方法在以下方面具有稳健性： 1. 配方在整个参数选择范围内的稳定性；和 2。对背景网格中界面的位置不敏感。我们推导出一个最优顺序先验误差估计并给出说明性的数值例子。