基于分级网格的有限体积元方法求解奇异摄动两点边值问题
The Finite Volume Element Method Based Improved Grade Mesh for the Singularly Perturbed Two-Point Boundary Value Problems
DOI: 10.12677/PM.2020.1010112, PDF,    国家自然科学基金支持
作者: 李 玲, 熊之光：湖南科技大学，数学与计算科学学院，湖南 湘潭
关键词: 奇异摄动两点边值问题；分级网格；有限体积元法；收敛性；Singularly Perturbed Two-Point Boundary Value Problems； Hierarchical Mesh； Finite Volume El-ement Method； Convergence
摘要: 针对一类奇异摄动两点边值问题，本文讨论了基于分级网格及其对偶网格的有限体积元法及其收敛性。在基于分级网格及其对偶网格的基函数及空间的基础上，推导了有限体积元方法的计算格式，所给例子表明所研究计算方法具有稳定和有效性。
Abstract: For a class of singularly perturbed two-point boundary value problems, the finite volume element method based on hierarchical meshes and their dual meshes and its convergence are discussed. Based on the basis function and space of the hierarchical grids and its dual grids, the calculation format of the finite volume element method is deduced. The examples given show that the proposed method is stable and effective.
文章引用：李玲, 熊之光. 基于分级网格的有限体积元方法求解奇异摄动两点边值问题[J]. 理论数学, 2020, 10(10): 962-968. https://doi.org/10.12677/PM.2020.1010112

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