Multigrid Methods for a Stabilized Reissner–Mindlin Plate Formulation

Schöberl, Joachim; Stenberg, Rolf

doi:10.1137/060672182

Cited by 5 publications

(1 citation statement)

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“…A recent stabilised alternative, using the same unknowns, has been developed in [18]. Finally, we mention the work [21] where a refined analysis of a family of stabilised methods and a multi grid algorithm are proposed. It is worth mentioning that none of these references deal with the system of first order equations, and then the bending moment tensor needs to be computed as the symmetric part of the gradient of the displacement vector multiplied by the appropriate physical constants.…”

Section: Introductionmentioning

confidence: 99%

Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model

Barrenechea

Barrios

Wachtel

2014

Calcolo

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This version is available at https://strathprints.strath.ac.uk/50948/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model * Gabriel R. Barrenechea † , Tomás P. Barrios ‡ , and Andreas Wachtel § , AbstractThis work presents new stabilised finite element methods for a bending moments formulation of the Reissner-Mindlin plate model. The introduction of the bending moment as an extra unknown leads to a new weak formulation, where the symmetry of this variable is imposed strongly in the space. This weak problem is proved to be well-posed, and stabilised Galerkin schemes for its discretisation are presented and analysed. The finite element methods are such that the bending moment tensor is sought in a finite element space constituted of piecewise linear continuos and symmetric tensors. Optimal error estimates are proved, and these findings are illustrated by representative numerical experiments.Mathematics Subject Classifications (1991):

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Section: Introductionmentioning

confidence: 99%