Nonconforming locking-free finite elements for Reissner–Mindlin plates

Chinosi, C.; Lovadina, Carlo; Marini, L. D.

doi:10.1016/j.cma.2005.06.025

Cited by 40 publications

(25 citation statements)

References 9 publications

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“…The computational cost for the standard approach and the mitc approach without bubble functions is the same, whereas the mitc approach with bubble functions has more degrees of freedom and therefore, is computationally more expensive than the other two approaches. Example 1 Our first numerical example is taken from Chinosi et al [9], where the exact solution for the transverse displacement is given by…”

Section: Numerical Resultsmentioning

confidence: 99%

A new MITC finite element method for Reissner--Mindlin plate problem based on a biorthogonal system

Lamichhane¹,

Meylan²

2017

ANZIAMJ

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Section: Numerical Resultsmentioning

confidence: 99%

A new MITC finite element method for Reissner--Mindlin plate problem based on a biorthogonal system

Lamichhane¹,

Meylan²

2017

ANZIAMJ

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“…See, for example, Arnold et al (2005), Arnold and Falk (1989), Brezzi and Marini (2003), Chinosi et al (2006), Lovadina (2005), and Ming and Shi (2001).…”

Section: Other Locking-free Elementsmentioning

confidence: 99%

Mixed Finite Element Methods

Auricchio

Veiga

Brezzi

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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Within the well‐known and highly effective finite element method for the computation of approximate solutions of complex boundary value problems, we focus on the often‐called mixed finite element methods , where in our terminology the word “mixed” indicates the fact that the problem discretization typically results in a linear algebraic system characterized by a null matrix on the main diagonal. Accordingly, the goals of the present article are (i) to sketch out that several physical problems share such an algebraic structure once a discretization is introduced; (ii) to present a simple, algebraic version of the abstract theory that rules most applications of mixed finite element methods; (iii) to give several examples of efficient mixed finite element methods; and (iv) finally, to give some hints on how to perform a stability and error analysis, focusing on a representative problem.

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“…The aim of this Note is to discuss some finite element schemes recently proposed and studied in [6], [9], and [12]. These elements are all based on a mixed nonconforming approach, and they have some features which seem to be favorable for a possible extension to the more complex (and more interesting) case of shell problems.…”

Section: Introductionmentioning

confidence: 99%

“…

We report on recent results about some nonconforming finite elements for plates, introduced and analyzed in [6], [12] and [9]. All the elements are locking-free and exhibit optimal convergence rates.

…”

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confidence: 99%