Title:         Interior estimates for a low order finite element method for
the Reissner-Mindlin plate

Authors:       Douglas N. Arnold and Xiaobo Liu

Source:        Advances in Computational Mathematics 7 (1997), pp. 337-360

Status:        Published

Abstract:  Interior error estimates are obtained for a low order
finite element introduced by Arnold and Falk for the Reissner-Mindlin
plates. It is proved that the approximation error of the finite element
solution in the interior domain is bounded above by two parts: one
measures the local approximability of the exact solution by the finite
element space and the other the global approximability of the finite
element method.  As an application, we show that for the soft simply
supported plate, the Arnold-Falk element still achieves an almost
optimal convergence rate in the energy norm away from the boundary
layer, even though optimal order convergence cannot hold globally due
to the boundary layer. Numerical results are given which support our
conclusion.

Keywords:      Reissner-Mindlin plate, boundary layer, mixed finite element,
interior error estimate

Subj. class.:  65N30,73K10

URL:           http://ima.umn.edu/~arnold/papers/rmint.pdf