The inf-sup test

Chapelle, Dominique; Bathe, Klaus‐Jürgen

doi:10.1016/0045-7949(93)90340-j

Cited by 293 publications

(292 citation statements)

References 6 publications

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“…This criterion is however impossible to prove for practical situations. This is why the numerical evaluation of the inf-sup condition has received considerable attention [11,10]. This numerical evaluation, although not equivalent to the analytical inf-sup, gives indications on whether (17) is fulfilled or not for a given set of finite element discretizations.…”

Section: Numerical Assessment Of the Inf-sup Conditionmentioning

confidence: 99%

“…On the basis of three or four results it can be predicted whether the inf-sup value is probably bounded from underneath or, on the contrary, goes down to zero when the mesh is refined. The reliability of this test is demonstrated on several examples of elements for incompressible elasticity problems in [11]. In the following section this test is used to check the behavior of proposed enrichment strategies.…”

Section: Numerical Assessment Of the Inf-sup Conditionmentioning

confidence: 99%

“…In the following section this test is used to check the behavior of proposed enrichment strategies. However, we follow [11] and use only S uu = Ω ∇u : ∇u dΩ instead of M uu in (18). In order to perform the numerical infsup test, a sequence of successive refined meshes is considered.…”

Section: Numerical Assessment Of the Inf-sup Conditionmentioning

confidence: 99%

“…The numerical test proposed in [11] consists in testing a particular formulation by calculating β using meshes of increasing refinement. On the basis of three or four results it can be predicted whether the inf-sup value is probably bounded from underneath or, on the contrary, goes down to zero when the mesh is refined.…”

Section: Numerical Assessment Of the Inf-sup Conditionmentioning

confidence: 99%

“…To prove that a displacement-pressure pair satisfies the inf-sup condition is not a trivial task. However, a numerical test has been proposed by Brezzi and Fortin [10] then by Chapelle et al [11], in order to draw a prediction on the fulfilment of the inf-sup. This test proved to be useful for the study of the stability of various mixed elements [12].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stability of incompressible formulations enriched with X-FEM

Legrain

Moës

Huerta

2008

Computer Methods in Applied Mechanics and Engineering

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The treatment of (near-)incompressibility is a major concern for applications involving rubber-like materials, or when important plastic flows occurs as in forming processes. The use of mixed finite element methods is known to prevent the locking of the finite element approximation in the incompressible limit. However, it also introduces a critical condition for the stability of the formulation, called the infsup or LBB condition. Recently, the finite element method has evolved with the introduction of the partition of unity. The eXtended Finite Element Method (X-FEM) uses the partition of unity to remove the need to mesh physical surfaces or to remesh them as they evolve. The enrichment of the displacement field makes it possible to treat surfaces of discontinuity inside finite elements. In this paper, some strategies are proposed for the enrichment of mixed finite element approximations in the incompressible setting. The case of holes, material interfaces and cracks are considered. Numerical examples show that for well chosen enrichment strategies, the finite element convergence rate is preserved and the inf-sup condition is passed.

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Section: Numerical Assessment Of the Inf-sup Conditionmentioning

confidence: 99%

Section: Numerical Assessment Of the Inf-sup Conditionmentioning

confidence: 99%

Section: Numerical Assessment Of the Inf-sup Conditionmentioning

confidence: 99%

Section: Numerical Assessment Of the Inf-sup Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability of incompressible formulations enriched with X-FEM

Legrain

Moës

Huerta

2008

Computer Methods in Applied Mechanics and Engineering

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Displacement/Pressure Based Mixed Finite Element Formulations for Acoustic Fluid-Structure Interaction Problems

Wang

Bathe

1997

Int. J. Numer. Meth. Engng.

136

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SUMMARYWe present reliable finite element discretizations based on displacement/pressure interpolations for the analysis of acoustic fluid-structure interaction problems. The finite element interpolations are selected using the inf-sup condition, and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation. We show that with our analysis procedure no spurious non-zero frequencies are encountered, as heretofore calculated with other displacement-based discretizations.1997 by John Wiley & Sons, Ltd.

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On evaluating the inf-sup condition for plate bending elements

Iosilevich

Bathe

Brezzi

1997

Int. J. Numer. Meth. Engng.

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This paper addresses the evaluation of the inf-sup condition for Reissner-Mindlin plate bending elements. This fundamental condition for stability and optimality of a mixed ÿnite element scheme is, in general, very diicult to evaluate analytically, considering for example distorted meshes. Therefore, we develop a numerical test methodology. To demonstrate the test methodology and to obtain speciÿc results, we apply it to standard displacement-based elements and elements of the MITC family. Whereas the displacement-based elements fail to satisfy the inf-sup condition, we ÿnd that the MITC elements pass our numerical test for uniform meshes and a sequence of distorted meshes. ?

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The inf-sup test

Cited by 293 publications

References 6 publications

Stability of incompressible formulations enriched with X-FEM

Stability of incompressible formulations enriched with X-FEM

Displacement/Pressure Based Mixed Finite Element Formulations for Acoustic Fluid-Structure Interaction Problems

On evaluating the inf-sup condition for plate bending elements

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