An Accurate Semi-Analytic Finite Difference Scheme for Two-Dimensional Elliptic Problems with Singularities

Z. Yosibash, M. Arad, A. Yakhot, G. Ben-Dor

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

A high-order semi-analytic finite difference scheme is presented to overcome degradation of numerical performance when applied to two-dimensional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional representation of the exact solution in the vicinity of the singularities, and a conventional finite difference scheme on the remaining domain. It is shown that the L-S SFDS is "pollution" free, i.e., no degradation in the convergence rate occurs because of the singularities, and the coefficients of the asymptotic solution in the vicinity of the singularities are computed as a by-product with a very high accuracy. Numerical examples for the Laplace and Poisson equations over domains containing re-entrant corners or abrupt changes in the boundary conditions are presented.

Original languageEnglish
Pages (from-to)281-296
Number of pages16
JournalNumerical Methods for Partial Differential Equations
Volume14
Issue number3
DOIs
StatePublished - 1 Jan 1998

Keywords

  • Elliptic PDE
  • High-order Finite Difference Schemes
  • Laplace equation
  • Singularities

Fingerprint

Dive into the research topics of 'An Accurate Semi-Analytic Finite Difference Scheme for Two-Dimensional Elliptic Problems with Singularities'. Together they form a unique fingerprint.

Cite this