Identification of Lamé parameters in linear elasticity: a fixed point approach

Mark S. Gockenbach; Akhtar A. Khan

doi:10.3934/jimo.2005.1.487

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2005, Volume 1, Issue 4: 487-497. Doi: 10.3934/jimo.2005.1.487

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Identification of Lamé parameters in linear elasticity: a fixed point approach

Mark S. Gockenbach^1, and
Akhtar A. Khan^2,

1.
Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295
2.
Department of Mathematics, University of Wisconsin-Barron County, 1800 College Drive, Rice Lake, WI 54868

Received: April 30, 2004

Revised: November 30, 2004

Published: September 2005

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Abstract

A fixed point iterative scheme is used for the simultaneous recovery of Lamé parameters in linear elasticity. Auxiliary problems principle applied to an output least-squares based regularized minimization problem results in a strongly convergent iterative scheme. When the (coefficient-dependent) energy norm is used, the condition ensuring the strong convergence are much milder and avoid any possibility of over-regularization.

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Mathematics Subject Classification: 35R, 49M, 65R.

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