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# High-Order Solution of Elliptic Partial Differential Equations in Domains Containing Conical Singularities

## Citation

Li, Zhiyi (2009) High-Order Solution of Elliptic Partial Differential Equations in Domains Containing Conical Singularities. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VEEB-AV75. https://resolver.caltech.edu/CaltechETD:etd-08042008-005339

## Abstract

In this thesis we introduce an algorithm, based on the boundary integral equation method, for the numerical evaluation of singular solutions of the Laplace equation in three dimensional space, with singularities induced by a conical point on an otherwise smooth boundary surface. This is a model version of a fundamental problem in science and engineering: accurate evaluation of solutions of Partial Differential Equations in domains whose boundaries contain geometric singularities. For simplicity we assume a small region near the conical point coincides with a straight cone of given cross section; otherwise the boundary surface is not restricted in any way. Our numerical results demonstrate excellent convergence as discretizations are refined, even at the singular point where the solutions tend to infinity.

Item Type: Thesis (Dissertation (Ph.D.)) Conical point; Integral equation; Partial Differential Equation; Singularity California Institute of Technology Engineering and Applied Science Applied And Computational Mathematics Public (worldwide access) Bruno, Oscar P. Bruno, Oscar P. (chair)Shepherd, Joseph E.Schroeder, PeterHou, Thomas Y. 28 July 2008 CaltechETD:etd-08042008-005339 https://resolver.caltech.edu/CaltechETD:etd-08042008-005339 10.7907/VEEB-AV75 No commercial reproduction, distribution, display or performance rights in this work are provided. 3013 CaltechTHESIS Imported from ETD-db 12 Aug 2008 26 Nov 2019 19:14

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