半规则网格条件下四阶椭圆方程的莫里有限元分析

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics Pub Date : 2024-10-21 DOI:10.21136/AM.2024.0103-24

Hiroki Ishizaka

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引用次数: 0

摘要

给出了Morley有限元法各向异性插值误差的精确估计，并将其应用于四阶椭圆方程。我们在分析中没有施加形状规则网格条件。各向异性网格可以用于此目的。本研究的主要贡献包括提供了术语一致性的新证明。这使我们能够获得各向异性一致性误差估计。证明的核心思想涉及到使用Raviart-Thomas和Morley有限元空间之间的关系。结果表明，改进的Morley有限元法可以有效地消除误差。

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Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition

We present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition in the analysis. Anisotropic meshes can be used for this purpose. The main contributions of this study include providing a new proof of the term consistency. This enables us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart-Thomas and Morley finite-element spaces. Our results indicate optimal convergence rates and imply that the modified Morley FEM may be effective for errors.

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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.