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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 9
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Original Articles

Bilateral estimates for solutions of boundary value problems in Kirchhoff plates

I. Chudinovich Department of Mathematical and Computer Sciences, University of Tulsa, Tulsa, OK, USA
,
C. Constanda Department of Mathematical and Computer Sciences, University of Tulsa, Tulsa, OK, USACorrespondence[email protected]
,
D. Doty Department of Mathematical and Computer Sciences, University of Tulsa, Tulsa, OK, USA
&
A. Koshchii Department of Computer Science, International Solomon University, Kharkov, Ukraine
Pages 1661-1674 | Received 17 Jan 2011, Accepted 06 Mar 2011, Published online: 22 Jun 2011
 
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Abstract

Dirichlet boundary value problems are studied for thin elastic plates on an elastic foundation within Kirchhoff's classical model. The aim is to construct dual problems that make it possible to obtain bilateral error estimates for approximate solutions. In the absence of an elastic foundation, the dual functionals are maximized on function sets whose elements satisfy certain differential restrictions. The theory is illustrated by means of a numerical example.

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