Interior Estimates for a Low Order Finite
Element Method for the Reissner-Mindlin Plate

Douglas N. Arnold
Deparpartment of Mathematics
Penn State University
University Park, PA 16802

Xiaobo Liu Deparpartment of Mathematics and Computer Science
Clarkson University
Box 5815
Potsdam, NY 13676-5815

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.

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

Subject classification: 65N30,73K10


Contributed June 28, 1996.