Dissertation/Thesis Abstract

On the Solution of Elliptic Partial Differential Equations on Regions with Corners
by Serkh, Kirill, Ph.D., Yale University, 2016, 117; 10160877
Abstract (Summary)

In this dissertation we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

Indexing (document details)
Advisor: Rokhlin, Vladimir
School: Yale University
School Location: United States -- Connecticut
Source: DAI-B 78/01(E), Dissertation Abstracts International
Subjects: Applied Mathematics
Keywords: Boundary Value Problems, Corners, Elliptic Partial Differential Equations, Numerical Analysis, Potential Theory, Singular Solutions
Publication Number: 10160877
ISBN: 978-1-369-15772-7
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