A posteriori error estimates for the Morley plate bending element

Veiga, L. Beirão da; Niiranen, Jarkko; Stenberg, Rolf

doi:10.1007/s00211-007-0066-1

Cited by 64 publications

(16 citation statements)

References 16 publications

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“…From ( The a posteriori error estimates for the Morley plate bending element have been studied, for example, see [7,20]. In the following we introduce the work in [20]:…”

Section: Asymptotic Lower Bounds For Eigenvaluesmentioning

confidence: 99%

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The lower bound property of the Morley element eigenvalues

Yang¹,

Li²,

Bi³

2016

Computers & Mathematics with Applications

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: In this paper, we prove that the Morley element eigenvalues approximate the exact ones from below on regular meshes, including adaptive local refined meshes, for the fourth-order elliptic eigenvalue problems with the clamped boundary condition in any dimension. And we implement the adaptive computation to obtain lower bounds of the Morley element eigenvalues for the vibration problem of clamped plate under tension.

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“…From ( The a posteriori error estimates for the Morley plate bending element have been studied, for example, see [7,20]. In the following we introduce the work in [20]:…”

Section: Asymptotic Lower Bounds For Eigenvaluesmentioning

confidence: 99%

“…A posteriori error estimates and adaptive methods of finite element approximation are topics attracting more attention from mathematical and physical fields (see, e.g., [1,2,6,8,12,15,16,18,26,34] and the references cited therein), and have also been applied to the Morley element method for plate problems (see, for example, [7,17,20,42]).…”

Section: Introductionmentioning

confidence: 99%

The lower bound property of the Morley element eigenvalues

Yang¹,

Li²,

Bi³

2016

Computers & Mathematics with Applications

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“…In the Kirchhoff-Love plate model, the biharmonic eigenvalue problem describes the vibration and buckling of an elastic plate subject to some certain boundary condition. The Morley element method is one of the most popular methods for this problem in applied mechanics and engineering, and was widely studied in literature, see [38,40,8,15,13,10,24,7,22,28] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

New Fourth Order Postprocessing Techniques for Plate Bending Eigenvalues by Morley Element

Ma¹,

Tian²

2021

Preprint

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In this paper, we propose and analyze the extrapolation methods and asymptotically exact a posterior error estimates for eigenvalues of the Morley element. We establish an asymptotic expansion of eigenvalues, and prove an optimal result for this expansion and the corresponding extrapolation method. We also design an asymptotically exact a posterior error estimate and propose new approximate eigenvalues with higher accuracy by utilizing this a posteriori error estimate. Finally, several numerical experiments are considered to confirm the theoretical results and compare the performance of the proposed methods.

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“…The Morley element was extended to arbitrarily dimensions by Wang and Xu [ 2 ] in 2006. For biharmonic equation, the a priori/a posteriori error estimate was studied in [ 3 – 6 ] and the convergence and optimality of the adaptive Morley element method was proved in [ 7 , 8 ]. The Morley element has been employed to solve the biharmonic eigenvalue problem, including the vibration of a plate; and [ 9 ] studied its a priori error estimate.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Morley element algorithms for the biharmonic eigenvalue problem

Yang

2018

J Inequal Appl

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This paper is devoted to the adaptive Morley element algorithms for a biharmonic eigenvalue problem in R n (n ≥ 2). We combine the Morley element method with the shifted-inverse iteration including Rayleigh quotient iteration and the inverse iteration with fixed shift to propose multigrid discretization schemes in an adaptive fashion. We establish an inequality on Rayleigh quotient and use it to prove the efficiency of the adaptive algorithms. Numerical experiments show that these algorithms are efficient and can get the optimal convergence rate. MSC: 65N25; 65N30; 65N15

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A posteriori error estimates for the Morley plate bending element

Abstract: A local a posteriori error indicator for the well known Morley element for the Kirchhoff plate bending problem is presented. The error indicator is proven to be both reliable and efficient. The technique applied is general and it is shown to have also other applications.

Cited by 64 publications

References 16 publications

The lower bound property of the Morley element eigenvalues

The lower bound property of the Morley element eigenvalues

New Fourth Order Postprocessing Techniques for Plate Bending Eigenvalues by Morley Element

Adaptive Morley element algorithms for the biharmonic eigenvalue problem

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