An heuristic finite difference scheme on irregular plane regions

Abstract

In this paper, we present an heuristic finite difference scheme for the second-order linear operator, which is derived from an unconstrained least squares problem defined by the consistency condition on the residuals of order one, two and three in the Taylor expansion of the local truncation error. It is based on a non-iterative calculation of the difference coefficients and can be used to solve efficiently Poisson-like equations on non-rectangular domains which are approximated by structured convex grids.