Interior estimates for a low order finite element method for the Reissner–Mindlin plate model |
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Authors: | Arnold Douglas N Liu Xiaobo |
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Institution: | (1) Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA;(2) Department of Mathematics and Computer Science, Clarkson University, Box 5815, Potsdam, NY 13676-5815, USA |
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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.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | Reissner– Mindlin plate boundary layer mixed finite element interior error estimate 65N30 73N10 |
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