Numerical Solution of Differential Equations in Irregular Plane Regions Using Quality Structured Convex Grids

Abstract: The variational grid generation method is a powerful tool for generating structured convex grids on irregular simply connected domains whose boundary is a polygonal Jordan curve. Several examples that show the accuracy of a difference approximation to the solution of a Poisson equation using these kind of structured grids have been recently reported. In this paper, we compare the accuracy of the numerical solution calculated by applying those structured grids with finite differences against the the solution obtained with Delaunay-like triangulations on irregular regions.