论文标题
弯曲的模拟有限差异方法：允许带有弯曲面的网格
The curved Mimetic Finite Difference method: allowing grids with curved faces
论文作者
论文摘要
我们为扩散问题提供了一种新的模拟有限差异方法，该方法在\ textit {curved}（即非平面）面上收敛于网格上。至关重要的是，它给出了一个对称离散问题，该问题仅使用一个弯曲面的一个离散未知的问题。我们构建核心的原理是放弃模拟有限差异方法的局部一致性的标准定义。相反，我们利用了$ p_ {0} $的新颖和全局概念 - 一致性。数值示例证实了带有随机扰动节点以及具有弯曲边界的网格的立方网格所提出的模拟方法的一致性和最佳收敛速率。
We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved face. The principle at the core of our construction is to abandon the standard definition of local consistency of mimetic finite difference methods. Instead, we exploit the novel and global concept of $P_{0}$-consistency. Numerical examples confirm the consistency and the optimal convergence rate of the proposed mimetic method for cubic grids with randomly perturbed nodes as well as grids with curved boundaries.
