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A Class of Immersed Finite Element Spaces and Their Application to Forward and Inverse Interface Problems

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dc.contributor.authorCamp, Brian Daviden
dc.contributor.committeechairLin, Taoen
dc.contributor.committeememberRogers, Robert C.en
dc.contributor.committeememberBeattie, Christopher A.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.committeememberAdjerid, Slimaneen
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:19:46Zen
dc.date.adate2003-12-08en
dc.date.available2014-03-14T20:19:46Zen
dc.date.issued2003-11-19en
dc.date.rdate2004-12-08en
dc.date.sdate2003-12-04en
dc.description.abstractA class of immersed finite element (IFE) spaces is developed for solving elliptic boundary value problems that have interfaces. IFE spaces are finite element approximation spaces which are based upon meshes that can be independent of interfaces in the domain. Three different quadratic IFE spaces and their related biquadratic IFE spaces are introduced here for the purposes of solving both forward and inverse elliptic interface problems in 1D and 2D. These different spaces are constructed by (i) using a hierarchical approach, (ii) imposing extra continuity requirements or (iii) using a local refinement technique. The interpolation properties of each space are tested against appropriate testing functions in 1D and 2D. The IFE spaces are also used to approximate the solution of a forward elliptic interface problem using the Galerkin finite element method and the mixed least squares finite element method. Finally, one appropriate space is selected to solve an inverse interface problem using either an output least squares approach or the least squares with mixed equation error method.en
dc.description.degreePh. D.en
dc.identifier.otheretd-12042003-220747en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-12042003-220747/en
dc.identifier.urihttp://hdl.handle.net/10919/29923en
dc.publisherVirginia Techen
dc.relation.haspartdissertation_brian_camp.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectmixed equation erroren
dc.subjectimmersed finite elementsen
dc.subjectelliptic interface problemen
dc.subjectleast squaresen
dc.subjectinverse problemsen
dc.titleA Class of Immersed Finite Element Spaces and Their Application to Forward and Inverse Interface Problemsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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