A family of higher order mixed finite element methods for plane elasticity

Douglas N. Arnold; Jim Douglas; Chaitan P. Gupta

doi:10.1007/BF01379659

A family of higher order mixed finite element methods for plane elasticity

Douglas N. Arnold, Jim Douglas, Chaitan P. Gupta

Mathematics

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Abstract

The Dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the Raviart-Thomas mixed finite elements for a scalar, second-order elliptic equation. Estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor in L²(Ω), and optimal order negative norm estimates are obtained in H^s(Ω)′ for a range of s depending on the index of the finite element space. An optimal order estimate in L^∞(Ω) for the displacement error is given. Also, a quasioptimal estimate is derived in an appropriate space. All estimates are valid uniformly with respect to the compressibility and apply in the incompressible case. The formulation of the elements is presented in detail.

Original language	English (US)
Pages (from-to)	1-22
Number of pages	22
Journal	Numerische Mathematik
Volume	45
Issue number	1
DOIs	https://doi.org/10.1007/BF01379659
State	Published - Feb 1984

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Subject Classifications: AMS(MOS): 65N30, CR: G 1.8

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A family of higher order mixed finite element methods for plane elasticity

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