Worcester Polytechnic Institute Electronic Theses and Dissertations Collection

Title page for ETD etd-120407-095718


Document Typedissertation
Author NameWasyk, Rebecca Dawn
Email Address rebecca.wasyk at gmail.com
URNetd-120407-095718
TitleNumerical Solution of a Transmission Problem with Prefractal Interface
DegreePhD
DepartmentMathematical Sciences
Advisors
  • Umberto Mosco, Advisor
  • Robert Gilbert, Committee Member
  • Marcus Sarkis, Committee Member
  • Bogdan Vernescu, Department Head
  • Homer Walker, Committee Member
  • Keywords
  • finite element
  • singularities
  • transmission
  • prefractal
  • fractal
  • Date of Presentation/Defense2007-10-26
    Availability unrestricted

    Abstract

    Certain physical problems in electrostatics, magnetostatics, and heat transfer give rise to elliptic boundary value problems with transmission conditions on a layer. We focus on a particular problem with a second order transmission condition, representing an infinitely conductive layer. To approximate irregular layers that may naturally arise, a sequence of layers that converge to the fractal von Koch curve is considered. The solution to this transmission problem with a prefractal layer exhibits singularities due to the transmission condition across the layer as well as the reentrant corners introduced in the domain by the prefractal curve. To solve this problem numerically using a finite element method, the mesh must be adjusted to account for these singularities. We exhibit a general algorithm for creating a finite element discretization of the domain that results in linear convergence of the numerical solution to the true solution in a suitable norm.

    Files
  • ThesisFinalDraft.pdf

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