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A posteriori error estimates for the Morley plate bending element

Authors:

L. Beirão da Veiga,

J. Niiranen,

R. StenbergAuthors Info & Claims

Numerische Mathematik, Volume 106, Issue 2

Pages 165 - 179

https://doi.org/10.1007/s00211-007-0066-1

Published: 27 March 2007 Publication History

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.

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Carstensen CPuttkammer S(2024)Adaptive guaranteed lower eigenvalue bounds with optimal convergence ratesNumerische Mathematik10.1007/s00211-023-01382-8156:1(1-38)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1007/s00211-023-01382-8
Li Y(2021)Recovery-based a Posteriori Error Analysis for Plate Bending ProblemsJournal of Scientific Computing10.1007/s10915-021-01595-988:3Online publication date: 3-Aug-2021
https://dl.acm.org/doi/10.1007/s10915-021-01595-9
Chen LHu JHuang X(2018)Multigrid Methods for Hellan---Herrmann---Johnson Mixed Method of Kirchhoff Plate Bending ProblemsJournal of Scientific Computing10.1007/s10915-017-0636-z76:2(673-696)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.1007/s10915-017-0636-z
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A posteriori error estimates for the Morley plate bending element

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Published In

Numerische Mathematik Volume 106, Issue 2

March 2007

181 pages

ISSN:0029-599X

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 27 March 2007

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Cited By

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Carstensen CPuttkammer S(2024)Adaptive guaranteed lower eigenvalue bounds with optimal convergence ratesNumerische Mathematik10.1007/s00211-023-01382-8156:1(1-38)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1007/s00211-023-01382-8
Li Y(2021)Recovery-based a Posteriori Error Analysis for Plate Bending ProblemsJournal of Scientific Computing10.1007/s10915-021-01595-988:3Online publication date: 3-Aug-2021
https://dl.acm.org/doi/10.1007/s10915-021-01595-9
Chen LHu JHuang X(2018)Multigrid Methods for Hellan---Herrmann---Johnson Mixed Method of Kirchhoff Plate Bending ProblemsJournal of Scientific Computing10.1007/s10915-017-0636-z76:2(673-696)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.1007/s10915-017-0636-z
Sun PHuang X(2018)Quasi-optimal convergence rate for an adaptive hybridizable $$C^0$$C0 discontinuous Galerkin method for Kirchhoff platesNumerische Mathematik10.1007/s00211-018-0953-7139:4(795-829)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.1007/s00211-018-0953-7
Yang YLi HBi H(2016)The lower bound property of the Morley element eigenvaluesComputers & Mathematics with Applications10.1016/j.camwa.2016.06.00472:4(904-920)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1016/j.camwa.2016.06.004
Shen Q(2015)A posteriori error estimates of the Morley element for the fourth order elliptic eigenvalue problemNumerical Algorithms10.1007/s11075-014-9854-868:3(455-466)Online publication date: 1-Mar-2015
https://dl.acm.org/doi/10.1007/s11075-014-9854-8
Li MGuan XMao S(2014)New error estimates of the Morley element for the plate bending problemsJournal of Computational and Applied Mathematics10.5555/2753880.2754143263:C(405-416)Online publication date: 1-Jun-2014
https://dl.acm.org/doi/10.5555/2753880.2754143
Carstensen CGallistl DHu J(2014)A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemesComputers & Mathematics with Applications10.1016/j.camwa.2014.07.01968:12(2167-2181)Online publication date: 1-Dec-2014
https://dl.acm.org/doi/10.1016/j.camwa.2014.07.019
Carstensen CGallistl DHu J(2013)A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectanglesNumerische Mathematik10.1007/s00211-012-0513-5124:2(309-335)Online publication date: 1-Jun-2013
https://dl.acm.org/doi/10.1007/s00211-012-0513-5
Beirão da Veiga LChinosi CLovadina CStenberg R(2008)A-priori and a-posteriori error analysis for a family of Reissner–Mindlin plate elements BIT10.1007/s10543-008-0175-y48:2(189-213)Online publication date: 1-Jun-2008
https://dl.acm.org/doi/10.1007/s10543-008-0175-y

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New error estimates of the Morley element for the plate bending problems

The Morley-Type Virtual Element for Plate Bending Problems

Residual-Based A Posteriori Error Estimate for a Nonconforming Reissner--Mindlin Plate Finite Element

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