Non-conforming finite element methods for transmission eigenvalue problem

Yang Yidu; Han Jiayu; Bi Hai

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Non-conforming finite element methods for transmission eigenvalue problem

机译：传输特征值问题的非协调有限元方法

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The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem, we give a weak formulation which is a nonselfadjoint linear eigenvalue problem. Based on the weak formulation, we first discuss the non-conforming finite element approximation, and prove the error estimates of the discrete eigenvalues obtained by the Adini element, the Morley-Zienkiewicz element, the modified-Zienkiewicz element et al. And we report some numerical examples to validate the efficiency of our approach for solving transmission eigenvalue problem. (C) 2016 Elsevier B.V. All rights reserved.

机译：传输特征值问题是逆散射理论中一个重要且具有挑战性的话题。在本文中，对于亥姆霍兹透射特征值问题，我们给出了一个弱公式，即非自伴线性特征值问题。基于弱公式，我们首先讨论了非协调有限元逼近，并证明了由Adini元素，Morley-Zienkiewicz元素，修改后的Zienkiewicz元素等获得的离散特征值的误差估计。并且我们报告了一些数值示例，以验证我们的方法解决传输特征值问题的效率。（C）2016 Elsevier B.V.保留所有权利。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2016年第1期|144-163|共20页
作者
Yang Yidu; Han Jiayu; Bi Hai;
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作者单位

Guizhou Normal Univ, Sch Math Sci, Guiyang 550001, Peoples R China;

Guizhou Normal Univ, Sch Math Sci, Guiyang 550001, Peoples R China;

Guizhou Normal Univ, Sch Math Sci, Guiyang 550001, Peoples R China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Transmission eigenvalue; The weak formulation; Non-conforming finite elements; Error estimates;

机译：传递特征值;弱公式;不合格有限元;误差估计;

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2. A two-grid discretization scheme of non-conforming finite elements for transmission eigenvalues [J] . Wang Shixi, Bi Hai, Zhang Yu, Computers & mathematics with applications . 2018,第2期

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3. Eigenvalue approximation by mixed non-conforming finite element methods The determination of the vibrational modes of a linear elastic solid [J] . Dello Russo Anahi Calcolo . 2014,第4期

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7. Non-conforming finite element methods for transmission eigenvalue problem [O] . Yang, Yidu, Han, Jiayu, Bi, Hai 2016

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8. Final Report for 'Non-Conforming Finite Elements; Mesh Generation, Adaptivity and Related Algebraic Multigrid and Domain Decomposition Methods in Massively Parallel Computing Environment [R] . Lazarov, R., Pasciak, J., Jones, J. 2002

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Non-conforming finite element methods for transmission eigenvalue problem

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