An Adaptive Finite Element Scheme for the Hellinger-Reissner Elasticity Mixed Eigenvalue Problem

Fleurianne Bertrand; Daniele Boffi; Rui Ma

doi:10.1515/cmam-2020-0034

An Adaptive Finite Element Scheme for the Hellinger-Reissner Elasticity Mixed Eigenvalue Problem

Fleurianne Bertrand^*
, Daniele Boffi
, Rui Ma

^*此作品的通讯作者

University of Twente
King Abdullah University of Science and Technology
University of Pavia
University of Duisburg-Essen

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

In this paper, we study the approximation of eigenvalues arising from the mixed Hellinger-Reissner elasticity problem by using a simple finite element introduced recently by one of the authors. We prove that the method converges when a residual type error estimator is considered and that the estimator decays optimally with respect to the number of degrees of freedom. A postprocessing technique originally proposed in a different context is discussed and tested numerically.

源语言	英语
页（从-至）	501-512
页数	12
期刊	Computational Methods in Applied Mathematics
卷	21
期	3
DOI	https://doi.org/10.1515/cmam-2020-0034
出版状态	已出版 - 1 7月 2021
已对外发布	是

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abstract = "In this paper, we study the approximation of eigenvalues arising from the mixed Hellinger-Reissner elasticity problem by using a simple finite element introduced recently by one of the authors. We prove that the method converges when a residual type error estimator is considered and that the estimator decays optimally with respect to the number of degrees of freedom. A postprocessing technique originally proposed in a different context is discussed and tested numerically.",

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AU - Boffi, Daniele

AU - Ma, Rui

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N2 - In this paper, we study the approximation of eigenvalues arising from the mixed Hellinger-Reissner elasticity problem by using a simple finite element introduced recently by one of the authors. We prove that the method converges when a residual type error estimator is considered and that the estimator decays optimally with respect to the number of degrees of freedom. A postprocessing technique originally proposed in a different context is discussed and tested numerically.

AB - In this paper, we study the approximation of eigenvalues arising from the mixed Hellinger-Reissner elasticity problem by using a simple finite element introduced recently by one of the authors. We prove that the method converges when a residual type error estimator is considered and that the estimator decays optimally with respect to the number of degrees of freedom. A postprocessing technique originally proposed in a different context is discussed and tested numerically.

KW - Hellinger-Reissner elasticity

KW - adaptive finite elements

KW - eigenvalue problem

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An Adaptive Finite Element Scheme for the Hellinger-Reissner Elasticity Mixed Eigenvalue Problem

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