TY - JOUR

T1 - An Accurate Semi-Analytic Finite Difference Scheme for Two-Dimensional Elliptic Problems with Singularities

AU - Yosibash, Z.

AU - Arad, M.

AU - Yakhot, A.

AU - Ben-Dor, G.

PY - 1998/5

Y1 - 1998/5

N2 - 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.

AB - 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.

KW - Elliptic PDE

KW - High-order Finite Difference Schemes

KW - Laplace equation

KW - Singularities

UR - http://www.scopus.com/inward/record.url?scp=1842632053&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1098-2426(199805)14:3<281::AID-NUM1>3.0.CO;2-I

DO - 10.1002/(SICI)1098-2426(199805)14:3<281::AID-NUM1>3.0.CO;2-I

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AN - SCOPUS:1842632053

SN - 0749-159X

VL - 14

SP - 281

EP - 296

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 3

ER -