On mixed finite element methods for the Reissner-Mindlin plate model
Ricardo G. Durán,Elsa Liberman +1 more
TLDR
In this article, the convergence of mixed finite element approximations to the Reissner-Mindlin plate problem is analyzed, and several known elements fall into the analysis, thus providing a unified approach.Abstract:
In this paper we analyze the convergence of mixed finite element approximations to the solution of the Reissner-Mindlin plate problem. We show that several known elements fall into our analysis, thus providing a unified approach. We also introduce a low-order triangular element which is optimalorder convergent uniformly in the plate thickness.read more
Citations
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Journal ArticleDOI
An isogeometric method for the Reissner–Mindlin plate bending problem
TL;DR: In this paper, a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem is presented, which follows a recent theoretical framework that makes possible the construction of a space of smooth discrete deflections Wh and a smooth discrete rotations Θh such that the Kirchhoff constraint is exactly satisfied at the limit.
Journal ArticleDOI
Multigrid methods for parameter dependent problems
TL;DR: In this paper, the authors discute des methodes multigrilles for les problemes dependant de parametres, and prouve que the diminution du nombre d'iterations des algorithmes est bornee independamment du parametre and du niveau de maillages, and ce dans un cadre general.
Journal ArticleDOI
A Family of Discontinuous Galerkin Finite Elements for the Reissner--Mindlin Plate
TL;DR: A family of locking-free elements for the Reissner–Mindlin plate is developed using Discontinuous Galerkin (DG) techniques, one for each odd degree, and optimal error estimates are proved.
Journal ArticleDOI
Locking-free Reissner-Mindlin elements without reduced integration
TL;DR: This work develops and analyze other families of locking free finite elements that eliminate the need for the introduction of a reduction operator, which has been a central feature of many locking-free methods.
Journal ArticleDOI
Preconditioning discrete approximations of the Reissner-Mindlin plate model
TL;DR: In this paper, the authors consider des methodes iteratives pour resoudre le systeme d'equations lineaires resultant de la discretisation par elements finis mixtes du modele de plaque de Reissner-Mindlin.
References
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Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Book
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
TL;DR: This paper presents the results of an analysis of the "Stream Function-Vorticity-Pressure" Method for the Stokes Problem in Two Dimensions and its applications to Mixed Approximation and Homogeneous Stokes Equations.
Book ChapterDOI
A mixed finite element method for 2-nd order elliptic problems
P. A. Raviart,J. M. Thomas +1 more
Journal ArticleDOI
Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
M. Crouzeix,P.-A. Raviart +1 more
TL;DR: Both conforming and nonconforming finite element methods are studied and various examples of simplicial éléments well suited for the numerical treatment of the incompressibility condition are given.
Journal ArticleDOI
A stable finite element for the stokes equations
TL;DR: In this paper, a new velocity-pressure finite element for the computation of Stokes flow is presented, which satisfies the usual inf-sup condition and converges with first order for both velocities and pressure.