A remark on finite element schemes for nearly incompressible elasticity

Daniele Boffi; Rolf Stenberg

doi:10.1016/j.camwa.2017.06.006

A remark on finite element schemes for nearly incompressible elasticity

Daniele Boffi^*, Rolf Stenberg

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

University of Pavia

Research output: Contribution to journal › Article › Scientific › peer-review

12 Citations (Scopus)

Abstract

In this paper we discuss mixed finite element methods for nearly incompressible elasticity. We show that if a method uses the hydrostatic pressure as unknown, then the finite element spaces have to satisfy the condition of the ellipticity on the kernel, in addition to the well-known Babuška–Brezzi condition. Some known elements are proved to satisfy this condition.

Original language	English
Pages (from-to)	2047-2055
Number of pages	9
Journal	Computers and Mathematics with Applications
Volume	74
Issue number	9
DOIs	https://doi.org/10.1016/j.camwa.2017.06.006
Publication status	Published - 1 Nov 2017
MoE publication type	A1 Journal article-refereed

Keywords

Incompressible elasticity
Mixed finite element methods
Stability conditions

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10.1016/j.camwa.2017.06.006

Cite this

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abstract = "In this paper we discuss mixed finite element methods for nearly incompressible elasticity. We show that if a method uses the hydrostatic pressure as unknown, then the finite element spaces have to satisfy the condition of the ellipticity on the kernel, in addition to the well-known Babu{\v s}ka–Brezzi condition. Some known elements are proved to satisfy this condition.",

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AU - Stenberg, Rolf

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AB - In this paper we discuss mixed finite element methods for nearly incompressible elasticity. We show that if a method uses the hydrostatic pressure as unknown, then the finite element spaces have to satisfy the condition of the ellipticity on the kernel, in addition to the well-known Babuška–Brezzi condition. Some known elements are proved to satisfy this condition.

KW - Incompressible elasticity

KW - Mixed finite element methods

KW - Stability conditions

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M3 - Article

AN - SCOPUS:85020854618

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SP - 2047

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 9

ER -

A remark on finite element schemes for nearly incompressible elasticity

Abstract

Keywords

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