A fourth order block-hexagonal grid approximation for the solution of Laplace’s equation with singularities

Abstract

The hexagonal grid version of the block-grid method, which is a difference-analytical method, has been applied for the solution of Laplace’s equation with Dirichlet boundary conditions, in a special type of polygon with corner singularities. It has been justified that in this polygon, when the boundary functions away from the singular corners are from the Hölder classes C4,λ, 0