四阶问题的Morley有限元及其Bell有限元方法
The Morley Element and Bell Element forFourth Order Elliptic Equations
DOI: 10.12677/PM.2023.1310317, PDF, 下载: 134  浏览: 213 
作者: 岳运：贵州大学数学与统计学院，贵州 贵阳
关键词: 重调和；有限元；Morley元；Bel1元；Biharmonic； Finite Element； Morley Fem； Bell Fem
摘要: 四阶问题又叫做重调和方程，起源于物理中连续介质力学领域的弹性薄板理论。对重调和方程的加速求解对许多实际问题，如工程建筑设计，流体力学等具有很重要的意义。本文主要讨论求解重调和问题的有限元方法，首先推导出其弱形式，利用morlev有限元空间，bel有限元空间逼近原方程的解空间，然后给出对应的L∞误差并且对比了两种方法的收敛阶。
Abstract: The fourth-order problem, also known as the reharmonic equation, originates from the elastic sheet theory in the field of continuum mechanics in physics. The accelerated solution of reharmonic equations is of great significance for many practical problems, such as engineering and architectural design and fluid mechanics. This paper focuses on the finite-element method for solving the reharmonic problem, first derive its weak form, using the morley finite-element space and the bell finite-element space approaching the solution space of the original equation,Then the corresponding L∞ error is given and the convergence order of the two methods is compared.
文章引用：岳运. 四阶问题的Morley有限元及其Bell有限元方法[J]. 理论数学, 2023, 13(10): 3071-3079. https://doi.org/10.12677/PM.2023.1310317

参考文献

[1] Kim, D., Pani, A.K. and Park, E.-J. (2021) Morley Finite Element Methods for the Stationary Quasi-Geostrophic Equation. Computer Methods in Applied Mechanics and Engineering, 375, Article 113639.
https://doi.org/10.1016/j.cma.2020.113639
[2] Saber, R. and Murray, R. (2003) Consensus Protocols for Networks of Dynamic Agents. Pro- ceedings of the 2003 American Control Conference, Denver, CO, 4-6 June 2003, 951-956.
https://doi.org/10.1109/ACC.2003.1239709
[3] 石钟慈.关于Morley元的误差估计[J].计算数学，1990.12(2): 113-118.
[4] Ming, W. and Xu, J. (2006) The Morley Element for Fourth Order Elliptic Equations in Any Dimensions. Numerische Mathematik, 103, 155-169.
https://doi.org/10.1007/s00211-005-0662-x

为你推荐