On the Solution of Elliptic Partial Differential Equations on Regions with Corners

Abstract

In this report 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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 09, 2015
Accession Number
AD1001119

Entities

People

  • Kirill Serkh
  • Vladimir Rokhlin, Jr.

Organizations

  • Yale University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Analytic Functions
  • Boundary Value Problems
  • Contour Integrals
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Helmholtz Equations
  • Identities
  • Integral Equations
  • Integrals
  • Linear Systems
  • Numbers
  • Partial Differential Equations
  • Potential Theory
  • Real Numbers
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)