Summary
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 inL 2(Ω), and optimal order negative norm estimates are obtained inH s(Ω)′ for a range ofs depending on the index of the finite element space. An optimal order estimate inL ∞(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.
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This work was performed while Professor Arnold was a NATO Postdoctoral Fellow
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Arnold, D.N., Douglas, J. & Gupta, C.P. A family of higher order mixed finite element methods for plane elasticity. Numer. Math. 45, 1–22 (1984). https://doi.org/10.1007/BF01379659
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DOI: https://doi.org/10.1007/BF01379659