论文标题
有限元素的错误抑制方法
Error Inhibiting Methods for Finite Elements
论文作者
论文摘要
有限差异方法（FD）是解决部分微分方程（PDE）的最古老，最简单的方法之一。块有限的差异方法（BFD）是FD方法，其中域被分为包含两个或多个网格点的块或单元格，与标准FD方法不同，每个网格点都使用了不同的方案。 在最近的作品中表明，BFD方案可能比其截断错误更准确。由于这些方案抑制截断误差的积累的能力，这些方法称为误差抑制方案（EIS）。 该手稿表明，我们的BFD方案可以被视为一种特定类型的不连续Galerkin（DG）方法。然后，我们使用标准DG程序证明了BFD方案的稳定性，同时使用类似傅立叶的分析来确定其最佳收敛速率。 我们在一个和二维中介绍了数值示例，以证明这些方案的功效。
Finite Difference methods (FD) are one of the oldest and simplest methods for solving partial differential equations (PDE). Block Finite Difference methods (BFD) are FD methods in which the domain is divided into blocks, or cells, containing two or more grid points, with a different scheme used for each grid point, unlike the standard FD method. It was shown in recent works that BFD schemes might be one to three orders more accurate than their truncation errors. Due to these schemes' ability to inhibit the accumulation of truncation errors, these methods were called Error Inhibiting Schemes (EIS). This manuscript shows that our BFD schemes can be viewed as a particular type of Discontinuous Galerkin (DG) method. Then, we prove the BFD scheme's stability using the standard DG procedure while using a Fourier-like analysis to establish its optimal convergence rate. We present numerical examples in one and two dimensions to demonstrate the efficacy of these schemes.
