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
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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.References
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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
- Email: brenner@math.lsu.edu
- Li-yeng Sung
- Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803
- Email: sung@math.lsu.edu
- Yi Zhang
- Affiliation: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803
- Email: yzhang24@math.lsu.edu
- Received by editor(s): November 13, 2010
- Received by editor(s) in revised form: November 14, 2010
- 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.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 1247-1262
- MSC (2010): Primary 65K15, 65N30
- DOI: https://doi.org/10.1090/S0025-5718-2012-02602-0
- MathSciNet review: 2904578