论文标题
破裂培养基中压力模型的切割有限元方法
A cut finite element method for a model of pressure in fractured media
论文作者
论文摘要
我们开发了一种强大的切割有限元方法，用于在裂缝介质中扩散模型，该模型由带有嵌入式裂纹的散装域组成。裂缝具有自己的压力场，可以以非常一般的方式切穿散装网眼。从覆盖域的通用背景散装网格开始，为界面和批量子域构建有限元空间，从而有效地计算了耦合项。裂纹压力场还使用散装网格进行表示。界面条件是文献中先前考虑的罗宾类型条件的普遍形式，该形式允许对整个裂缝的一系列流动范围进行建模。该方法以以下方式具有鲁棒性：1。在参数选择的全部范围内配方的稳定性；和2。对界面在背景网格中的位置不敏感。我们得出了一个最佳的先验误差估计，并说明了数字示例。
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.
