Title page for ETD etd-12042003-220747


Type of Document Dissertation
Author Camp, Brian David
URN etd-12042003-220747
Title A Class of Immersed Finite Element Spaces and Their Application to Forward and Inverse Interface Problems
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Lin, Tao Committee Chair
Adjerid, Slimane Committee Member
Beattie, Christopher A. Committee Member
Borggaard, Jeffrey T. Committee Member
Rogers, Robert C. Committee Member
Keywords
  • mixed equation error
  • immersed finite elements
  • elliptic interface problem
  • least squares
  • inverse problems
Date of Defense 2003-11-19
Availability unrestricted
Abstract
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.

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