Nonconforming mixed finite element methods for linear elasticity using rectangular elements in two and three dimensions

Yi, Son-Young

doi:10.1007/s10092-005-0101-5

Cited by 50 publications

(36 citation statements)

References 18 publications

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“…21 In this paper, we propose a new stable pair of finite elements using rectangular elements. We approximate the normal traction by the lowest order element of the second family of mixed finite elements proposed by Nédélec 17 and the shear stress by a nonconforming subspace of H 1 (Ω).…”

Section: Introductionmentioning

confidence: 99%

A New Nonconforming Mixed Finite Element Method for Linear Elasticity

2006

Math. Models Methods Appl. Sci.

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We have developed new nonconforming mixed finite element methods for linear elasticity with a pure traction (displacement) boundary condition based on the Hellinger-Reissner variational principle using rectangular elements. Convergence analysis yields an optimal (suboptimal) convergence rate of O(h 2 ) (O(h 3 2 )) for the L 2 -error of the stress and O(h) for the displacement in the pure traction (displacement) boundary problem. However, numerical experiments have yielded optimal-order convergence rates for both stress and displacement in both problems and have shown superconvergence for the displacement at the midpoint of each element. Moreover, we observed that the optimal convergence rates are still valid for large λ.

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Section: Introductionmentioning

confidence: 99%

A New Nonconforming Mixed Finite Element Method for Linear Elasticity

2006

Math. Models Methods Appl. Sci.

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“…Many authors have developed mixed elements with weak symmetry, 2,6,26,28,27,24,8,9,17,20,15,19 which we will not pursue here. For nonconforming methods with strong symmetry, which is the subject of this paper, there have been several elements proposed for rectangular meshes, 29,30,21,12,23 but very little work on simplicial meshes. A two-dimensional nonconforming element of low degree was developed by two of the present authors.…”

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confidence: 99%

Nonconforming Tetrahedral Mixed Finite Elements for Elasticity

Arnold

Awanou

Winther

2014

Math. Models Methods Appl. Sci.

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Communicated by F. BrezziThis paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, and which is significantly simpler than any stable conforming mixed finite element method. The method may be viewed as the three-dimensional analogue of a previously developed element in two dimensions. As in that case, a variant of the method is proposed as well, in which the displacement approximation is reduced to piecewise rigid motions and the stress space is reduced accordingly, but the linear convergence is retained.

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“…These elements exhibit O(h) convergence rate for both the stress and displacement and can be written as part of a discrete version of the elasticity sequence. In [31] [33]. None of the three-dimensional nonconforming rectangular elements have been shown to be part of a discrete version of the elasticity sequence, that is an analogue of (16).…”

Section: Nonconforming Elementsmentioning

confidence: 99%

Symmetric Matrix Fields in the Finite Element Method

Awanou

2010

Symmetry

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The theory of elasticity is used to predict the response of a material body subject to applied forces. In the linear theory, where the displacement is small, the stress tensor which measures the internal forces is the variable of primal importance. However the symmetry of the stress tensor which expresses the conservation of angular momentum had been a challenge for finite element computations. We review in this paper approaches based on mixed finite element methods.

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Nonconforming mixed finite element methods for linear elasticity using rectangular elements in two and three dimensions

Cited by 50 publications

References 18 publications

A New Nonconforming Mixed Finite Element Method for Linear Elasticity

A New Nonconforming Mixed Finite Element Method for Linear Elasticity

Nonconforming Tetrahedral Mixed Finite Elements for Elasticity

Symmetric Matrix Fields in the Finite Element Method

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