含薄单元网格有限元解的误差估计

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics Pub Date : 2024-10-14 DOI:10.21136/AM.2024.0047-24

Kenta Kobayashi, Takuya Tsuchiya

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引用次数: 0

摘要

在泊松方程有限元解的误差估计中，我们通常对要使用的网格施加形状规则性假设。本文证明了即使不符合形状规则性条件，如果满足最小角度条件的简式虚拟地覆盖了违反形状规则性条件或最大角度条件的“坏”单元，也可以得到标准误差估计。数值实验验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Error estimation for finite element solutions on meshes that contain thin elements

In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if “bad” elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result.

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来源期刊

Applications of Mathematics 数学-应用数学

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering. The main topics covered include: - Mechanics of Solids; - Fluid Mechanics; - Electrical Engineering; - Solutions of Differential and Integral Equations; - Mathematical Physics; - Optimization; - Probability Mathematical Statistics. The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.