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Finite element methods for the displacement obstacle problem of clamped plates

Authors: Susanne C. Brenner, Li-yeng Sung and Yi Zhang
Journal: Math. Comp. 81 (2012), 1247-1262
MSC (2010): Primary 65K15, 65N30
Published electronically: February 29, 2012
MathSciNet review: 2904578
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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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Additional Information

Susanne C. Brenner
Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803

Li-yeng Sung
Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803

Yi Zhang
Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803

Keywords: Displacement obstacle, clamped Kirchhoff plate, fourth order, variational inequality, finite element, discontinuous Galerkin
Received by editor(s): November 13, 2010
Received by editor(s) in revised form: November 14, 2010, and May 4, 2011
Published electronically: February 29, 2012
Additional Notes: This work was supported in part by the National Science Foundation under Grant No. DMS-10-16332 and by the Institute for Mathematics and its applications with funds provided by the National Science Foundation.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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