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Stabilized variational formulation f...

Babaniyi, Olalekan Adeoye.

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Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities./
作者:	Babaniyi, Olalekan Adeoye.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:	134 p.
附註:	Source: Dissertation Abstracts International, Volume: 77-07(E), Section: B.
Contained By:	Dissertation Abstracts International77-07B(E).
標題:	Mechanical engineering. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10017004
ISBN:	9781339499475

Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.
Babaniyi, Olalekan Adeoye.

Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 134 p.

Source: Dissertation Abstracts International, Volume: 77-07(E), Section: B.

Thesis (Ph.D.)--Boston University, 2016.

We consider the design of finite element methods for inverse problems with full-field data governed by elliptic forward operators. Such problems arise in applications in inverse heat conduction, in mechanical property characterization, and in medical imaging. For this class of problems, novel finite element methods have been proposed (Barbone et al., 2010) that give good performance, provided the solutions are in the H1(O) function space. The material property distributions being estimated can be discontinuous, however, and therefore it is desirable to have formulations that can accommodate discontinuities in both data and solution. Toward this end, we present a mixed variational formulation for this class of problems that handles discontinuities well. We motivate the mixed formulation by examining the possibility of discretizing using a discontinuous discretization in an irreducible finite element method, and discuss the limitations of that approach. We then derive a new mixed formulation based on a least-square error in the constitutive equation. We prove that the continuous variational formulations are well-posed for applications in both inverse heat conduction and plane stress elasticity. We derive a priori error bounds for discretization error, valid in the limit of mesh refinement. We demonstrate convergence of the method with mesh refinement in cases with both continuous and discontinuous solutions. Finally we apply the formulation to measured data to estimate the elastic shear modulus distributions in both tissue mimicking phantoms and in breast masses from data collected in vivo.

ISBN: 9781339499475Subjects--Topical Terms:

649730
Mechanical engineering.

Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.
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