Guaranteed Lower Bounds for Eigenvalues of Elliptic Operators

Jun Hu; Yunqing Huang; Rui Ma

doi:10.1007/s10915-015-0126-0

Guaranteed Lower Bounds for Eigenvalues of Elliptic Operators

Jun Hu, Yunqing Huang, Rui Ma^*

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

13 引用（Scopus）

摘要

In this paper, we provide a method to produce guaranteed lower bounds for eigenvalues of 2m-th order elliptic operators in n dimensions for m≤ n, especially for elliptic operators with variable coefficients. This method is based on the corresponding Morley–Wang–Xu elements in literature and a unified way to estimate the explicit constants related to the L² error estimates for the interpolation of Morley–Wang–Xu elements.

源语言	英语
页（从-至）	1181-1197
页数	17
期刊	Journal of Scientific Computing
卷	67
期	3
DOI	https://doi.org/10.1007/s10915-015-0126-0
出版状态	已出版 - 1 6月 2016
已对外发布	是

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Hu, J., Huang, Y., & Ma, R. (2016). Guaranteed Lower Bounds for Eigenvalues of Elliptic Operators. Journal of Scientific Computing, 67(3), 1181-1197. https://doi.org/10.1007/s10915-015-0126-0

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abstract = "In this paper, we provide a method to produce guaranteed lower bounds for eigenvalues of 2m-th order elliptic operators in n dimensions for m≤ n, especially for elliptic operators with variable coefficients. This method is based on the corresponding Morley–Wang–Xu elements in literature and a unified way to estimate the explicit constants related to the L2 error estimates for the interpolation of Morley–Wang–Xu elements.",

keywords = "Eigenvalue problem, Lower bound, Nonconforming finite element",

author = "Jun Hu and Yunqing Huang and Rui Ma",

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AU - Huang, Yunqing

AU - Ma, Rui

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N2 - In this paper, we provide a method to produce guaranteed lower bounds for eigenvalues of 2m-th order elliptic operators in n dimensions for m≤ n, especially for elliptic operators with variable coefficients. This method is based on the corresponding Morley–Wang–Xu elements in literature and a unified way to estimate the explicit constants related to the L2 error estimates for the interpolation of Morley–Wang–Xu elements.

AB - In this paper, we provide a method to produce guaranteed lower bounds for eigenvalues of 2m-th order elliptic operators in n dimensions for m≤ n, especially for elliptic operators with variable coefficients. This method is based on the corresponding Morley–Wang–Xu elements in literature and a unified way to estimate the explicit constants related to the L2 error estimates for the interpolation of Morley–Wang–Xu elements.

KW - Eigenvalue problem

KW - Lower bound

KW - Nonconforming finite element

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Guaranteed Lower Bounds for Eigenvalues of Elliptic Operators

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