TY - JOUR

T1 - Analysis of a linear-linear finite element for the reissner-mindlin plate model

AU - Arnold, Douglas N.

AU - Falk, Richard S.

PY - 1997/3

Y1 - 1997/3

N2 - An analysis is presented for a recently proposed finite element method for the Reissner-Mindlin plate problem. The method is based on the standard variational principle, uses nonconforming linear elements to approximate the rotations and conforming linear elements to approximate the transverse displacements, and avoids the usual "locking problem" by interpolating the shear stress into a rotated space of lowest order Raviart-Thomas elements. When the plate thickness t = O(h), it is proved that the method gives optimal order error estimates uniform in t. However, the analysis suggests and numerical calculations confirm that the method can produce poor approximations for moderate sized values of the plate thickness. Indeed, for t fixed, the method does not converge as the mesh size h tends to zero.

AB - An analysis is presented for a recently proposed finite element method for the Reissner-Mindlin plate problem. The method is based on the standard variational principle, uses nonconforming linear elements to approximate the rotations and conforming linear elements to approximate the transverse displacements, and avoids the usual "locking problem" by interpolating the shear stress into a rotated space of lowest order Raviart-Thomas elements. When the plate thickness t = O(h), it is proved that the method gives optimal order error estimates uniform in t. However, the analysis suggests and numerical calculations confirm that the method can produce poor approximations for moderate sized values of the plate thickness. Indeed, for t fixed, the method does not converge as the mesh size h tends to zero.

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U2 - 10.1142/S0218202597000141

DO - 10.1142/S0218202597000141

M3 - Article

AN - SCOPUS:0031501260

SN - 0218-2025

VL - 7

SP - 217

EP - 238

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 2

ER -