About: Influence of mesh-dependent Korn's inequality on the convergence of nonconforming finite element schemes     Goto   Sponge   NotDistinct   Permalink

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Description
  • Diskutujeme platnost diskrétní analogie první Kornovy nerovnosti pro dvourozměrné nekonformní konečné prvky. Pro Crouzeixův-Raviartův prvek a rotovaný bilineární prvek závisí konstanta v této nerovnosti na síti a vyšetřujeme její vliv na konvergenční vlastnosti diskretizací Stokesových rovnic zahrnujících formulaci Laplaceova operátoru založenou na tenzoru deformace. Zatímco pro rotovaný bilineární prvek lze dokázat výsledky o konvergenci, v případě aplikace Crouzeixova-Raviartova konečného prvku nelze konvergenci očekávat. (cs)
  • We discuss the validity of a discrete analogue of Korn's first inequality for two-dimensional nonconforming finite elements. For the Crouzeix-Raviart element and the rotated bilinear element, the constant in this inequality is mesh-dependent and we investigate its influence on the convergence properties of finite element discretizations of the Stokes equations involving deformation tensor formulation of the Laplace operator. Whereas for the rotated bilinear element convergence results can be proved, no convergence of the standard discretization can be expected if the Crouzeix-Raviart element is applied.
  • We discuss the validity of a discrete analogue of Korn's first inequality for two-dimensional nonconforming finite elements. For the Crouzeix-Raviart element and the rotated bilinear element, the constant in this inequality is mesh-dependent and we investigate its influence on the convergence properties of finite element discretizations of the Stokes equations involving deformation tensor formulation of the Laplace operator. Whereas for the rotated bilinear element convergence results can be proved, no convergence of the standard discretization can be expected if the Crouzeix-Raviart element is applied. (en)
Title
  • Influence of mesh-dependent Korn's inequality on the convergence of nonconforming finite element schemes
  • Vliv na síti závisející Kornovy nerovnosti na konvergenci nekonformních schémat ve metodě konečných prvků (cs)
  • Influence of mesh-dependent Korn's inequality on the convergence of nonconforming finite element schemes (en)
skos:prefLabel
  • Influence of mesh-dependent Korn's inequality on the convergence of nonconforming finite element schemes
  • Vliv na síti závisející Kornovy nerovnosti na konvergenci nekonformních schémat ve metodě konečných prvků (cs)
  • Influence of mesh-dependent Korn's inequality on the convergence of nonconforming finite element schemes (en)
skos:notation
  • RIV/00216208:11320/05:00001288!RIV06-MSM-11320___
http://linked.open.../vavai/riv/strany
  • 85;95
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  • P(GA201/02/0684), Z(MSM 113200007)
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  • 524747
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  • RIV/00216208:11320/05:00001288
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  • Influence; mesh-dependent; Korn's; inequality; convergence; nonconforming; finite; element; schemes (en)
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  • [D58AA1166976]
http://linked.open...v/mistoKonaniAkce
  • Praha
http://linked.open...i/riv/mistoVydani
  • Praha
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  • Proceedings of Czech-Japanese Seminar in Applied Mathematics 2004
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  • Knobloch, Petr
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number of pages
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  • České vysoké učení technické v Praze
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  • 80-01-03181-0
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  • 11320
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