SIAM Journal on Numerical Analysis, Volume 59, Issue 1, Page 195-218, January 2021.
This paper deals with the derivation and analysis of reduced order elliptic PDE models on fractured domains. We use a Fourier analysis to obtain coupling conditions between subdomains when the fracture is represented as a hypersurface embedded in the surrounded rock matrix. We compare our results to prominent examples from the literature for diffusive models. In a second step, we present error estimates for the reduced order models in terms of the fracture width. For the proofs, we rely on a combination of Fourier analysis, asymptotic expansions, and functional analysis. Finally, we study the behavior of the error of the reduced order solutions on numerical test cases when the fracture width tends to zero.

中文翻译：

---

离散断裂矩阵模型中耦合的建模与分析

SIAM数值分析杂志，第59卷，第1期，第195-218页，2021年1月。
本文讨论了在断裂域上的降阶椭圆PDE模型的推导和分析。当将裂缝表示为嵌入在围岩矩阵中的超表面时，我们使用傅里叶分析获得子域之间的耦合条件。我们将我们的结果与扩散模型文献中的突出例子进行比较。在第二步中，我们根据裂缝宽度给出了降阶模型的误差估计。对于证明，我们依靠傅立叶分析，渐近展开和函数分析的组合。最后，我们研究了当断裂宽度趋于零时，在数值测试案例中降阶解的误差行为。