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.

翻译：有限差分法（FD）是求解偏微分方程最古老且最简单的数值方法之一。块有限差分法（BFD）是一种FD方法，它将求解域划分为包含两个或更多网格点的块（或单元），并对每个网格点采用不同的差分格式，这与标准FD方法不同。近期研究表明，BFD格式的精度可能比其截断误差高出一到三个数量级。由于这类格式能够抑制截断误差的累积，因此被称为误差抑制格式（EIS）。本文证明，我们的BFD格式可视为间断伽辽金（DG）方法的一种特殊形式。随后，我们采用标准DG过程验证BFD格式的稳定性，并通过类傅里叶分析建立其最优收敛阶。文中给出了一维和二维数值算例，以证明这些格式的有效性。