Finite element methods for the displacement obstacle problem of clamped plates

Brenner, Susanne; Sung, Li-yeng; Zhang, Yi

doi:10.1090/S0025-5718-2012-02602-0

Finite element methods for the displacement obstacle problem of clamped plates
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by Susanne C. Brenner, Li-yeng Sung and Yi Zhang PDF

Math. Comp. 81 (2012), 1247-1262 Request permission

Abstract:

We study finite element methods for the displacement obstacle problem of clamped Kirchhoff plates. A unified convergence analysis is provided for $C^1$ finite element methods, classical nonconforming finite element methods and $C^0$ interior penalty methods. Under the condition that the obstacles are sufficiently smooth and that they are separated from each other and the zero displacement boundary constraint, we prove that the convergence in the energy norm is $O(h)$ for convex domains.

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