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dc.contributor.authorBabaniyi, Olalekanen_US
dc.date.accessioned2016-02-29T16:37:52Z
dc.date.available2016-02-29T16:37:52Z
dc.date.issued2016
dc.identifier.urihttps://hdl.handle.net/2144/14640
dc.description.abstractWe 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 H^1(Ω) 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.en_US
dc.language.isoen_US
dc.rightsAttribution 4.0 Internationalen_US
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectMechanical engineeringen_US
dc.subjectBiomechanical imagingen_US
dc.subjectDirect methodsen_US
dc.subjectElastographyen_US
dc.subjectInverse elasticityen_US
dc.subjectInverse heat conductionen_US
dc.subjectStabilized variational formulationsen_US
dc.titleStabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuitiesen_US
dc.typeThesis/Dissertationen_US
dc.date.updated2016-02-17T23:19:14Z
etd.degree.nameDoctor of Philosophyen_US
etd.degree.leveldoctoralen_US
etd.degree.disciplineMechanical Engineeringen_US
etd.degree.grantorBoston Universityen_US


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Attribution 4.0 International
Except where otherwise noted, this item's license is described as Attribution 4.0 International