Area control in generating smooth and convex grids over general plane regions

A new method (adaptive smoothness functional) to produce convex and smooth grids over general plane regions has been introduced in a recent work by the authors [10]; this method belongs to the variational grid generation approach. Theoretical results showing that a convex grid over a region is obtained when this method is applied, were presented; the basic assumption was that at least one convex grid exists. A procedure to control large cells (bilateral smoothness functional), in addition to smoothness and convexity, was also presented. Experimental results, showing the effectiveness of these methods, were reported; however, no theoretical results were reported assuring that the area control can be always exerted. This article continues the same line of research, introducing a new version of the bilateral smoothness functional that improves the control of large areas. Unlike the former method, theoretical results show the effectiveness of the new bilateral smoothness functional to exert such control. Optimal grids obtained with the new functional are compared with those reached using the older version, demostrating the improvement.