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 -