Faculty Advisor

Homer Walker

Faculty Advisor

Umberto Mosco

Faculty Advisor

Robert Gilbert

Faculty Advisor

Marcus Sarkis

Faculty Advisor

Bogdan Vernescu

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."

Publisher

Worcester Polytechnic Institute

Degree Name

PhD

Department

Mathematical Sciences

Project Type

Dissertation

Date Accepted

2007-12-04

Accessibility

Unrestricted

Subjects

finite element, singularities, transmission, prefractal, fractal

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