A mixed least squares method for solving problems in linear elasticity: theoretical study |
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Authors: | M Tchonkova S Sture |
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Affiliation: | (1) ExxonMobil Upstream Research Company, P. O. Box 2189, Houston, TX 77252-2189, formerly: Research Associate, University of Colorado at Boulder, US;(2) Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, CO 80309-0428, US |
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Abstract: | In a previous paper we proposed a mixed least squares method for solving problems in linear elasticity. The solution to the
equations of linear elasticity was obtained via minimization of a least squares functional depending on displacements and
stresses. The performance of the method was tested numerically for low order elements for classical examples with well known
analytical solutions. In this paper we derive a condition for the existence and uniqueness of the solution of the discrete
problem for both compressible and incompressible cases, and verify the uniqueness of the solution analytically for two low
order piece-wise polynomial FEM spaces.
Received: 20 January 2001 / Accepted: 14 June 2002
The authors gratefully acknowledge the financial support provided by NASA George C. Marshall Space Flight Centre under contract
number NAS8-38779. |
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Keywords: | Least squares method Finite element method Elasticity Mixed methods |
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