A fourth-order accurate composite grid method for solving laplace's boundary value problems with singularities

Abstract

A fourth-order order accurate composite grid method is constructed and justified on graduated polygons by using a nine-point scheme on polar and square grids and constructing a fourth-order matching operator connecting the resulting subsystems. An estimate is obtained for the absolute error in maximum norm under constraints on the functions imposed by the boundary conditions that cannot be substantially weakened in C<inf>k, ?</inf>. Finally, the high accuracy of the method is illustrated by solving a problem defined on an L-shaped polygon with a corner singularity and the well-known Motz problem, which has a singularity due to abrupt changes in the type of boundary conditions. Copyright © 2002 by MAIK "Nauka/Interperiodica".