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

A 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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2003

Author dc:creator

• Camp, Brian David

Chair dc:contributor.committeechair

• Lin, Tao

Committee members dc:contributor.committeemember

• Rogers, Robert C.
• Beattie, Christopher A.
• Borggaard, Jeffrey T.
• Adjerid, Slimane

• mixed equation error
• immersed finite elements
• elliptic interface problem
• least squares
• inverse problems

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-12042003-220747

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/29923