The Laplacian method, initially introduced in Alexiadis et al. 2013 (1), is here extended to 2D cases. The solution algorithm on which the method is based is modified in order to tackle the issue of numerical noise in 2D domains. We also introduce the idea of the hybrid taxonomy and of hybrid-hybrid methods. The connection of the hybrid taxonomy with the notion of scale inheritance is discussed and the role of the Laplacian method within the taxonomy highlighted.