Show simple item record

dc.contributor.authorCamp, Brian Daviden_US
dc.date.accessioned2014-03-14T20:19:46Z
dc.date.available2014-03-14T20:19:46Z
dc.date.issued2003-11-19en_US
dc.identifier.otheretd-12042003-220747en_US
dc.identifier.urihttp://hdl.handle.net/10919/29923
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_US
dc.publisherVirginia Techen_US
dc.relation.haspartdissertation_brian_camp.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectmixed equation erroren_US
dc.subjectimmersed finite elementsen_US
dc.subjectelliptic interface problemen_US
dc.subjectleast squaresen_US
dc.subjectinverse problemsen_US
dc.titleA Class of Immersed Finite Element Spaces and Their Application to Forward and Inverse Interface Problemsen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairLin, Taoen_US
dc.contributor.committeememberRogers, Robert C.en_US
dc.contributor.committeememberBeattie, Christopher A.en_US
dc.contributor.committeememberBorggaard, Jeffrey T.en_US
dc.contributor.committeememberAdjerid, Slimaneen_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-12042003-220747/en_US
dc.date.sdate2003-12-04en_US
dc.date.rdate2004-12-08
dc.date.adate2003-12-08en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record