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^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1181-1197
Number of pages	17
Journal	Journal of Scientific Computing
Volume	67
Issue number	3
DOIs	https://doi.org/10.1007/s10915-015-0126-0
Publication status	Published - 1 Jun 2016
Externally published	Yes

Keywords

Eigenvalue problem
Lower bound
Nonconforming finite element

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10.1007/s10915-015-0126-0

Cite this

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title = "Guaranteed Lower Bounds for Eigenvalues of Elliptic Operators",

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 - Hu, Jun

AU - Huang, Yunqing

AU - Ma, Rui

PY - 2016/6/1

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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

UR - https://www.scopus.com/pages/publications/84947440516

U2 - 10.1007/s10915-015-0126-0

DO - 10.1007/s10915-015-0126-0

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SP - 1181

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JO - Journal of Scientific Computing

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IS - 3

ER -

Guaranteed Lower Bounds for Eigenvalues of Elliptic Operators

Abstract

Keywords

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