Linear Systems Arising for Second-Order Mimetic Divergence and Gradient Discretizations
Linear Systems Arising for Second-Order Mimetic Divergence and Gradient Discretizations
复制标题
二阶拟态散度和梯度离散化的线性系统
DOI：
10.1007/s10852-004-3523-1
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Mark Yasuda
中科院分区：
文献类型：
--
作者：
J. Castillo;Mark Yasuda
Castillo和Grone最近的研究导致了一种新的方法来构造散度和梯度算子的模拟离散化。他们的技术，采用矩阵公式，将模仿的约束，是能够产生近似的顺序在网格边界等于在网格的内部。在本文中，我们使用Castillo和Grone的方法构造了一个二阶拟离散，并通过将其应用于一维椭圆边值问题，将其与其他二阶离散进行了比较。提供了详细的扰动分析，以提供对研究中产生最佳数值结果的两种离散化的一些见解。
Recent investigations by Castillo and Grone have led to a new method for constructing mimetic discretizations of divergence and gradient operators. Their technique, which employs a matrix formulation to incorporate mimetic constraints, is capable of producing approximations whose order at a grid boundary is equal to that in the grid’s interior. In this paper, we construct a second-order mimetic discretization using Castillo and Grone’s approach and compare it to other second-order discretizations by applying them to an elliptic boundary value problem in one dimension. A detailed perturbation analysis is provided to offer some insight into the two discretizations yielding the best numerical results in the study.