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The goal of this article is to clarify some misunderstandings andinappropriate claims made in [6] regarding the relation between the weakGalerkin (WG) finite element method and the hybridizable discontinuous Galerkin(HDG). In this paper, the authors offered their understandings andinterpretations on the weak Galerkin finite element method by describing thebasics of the WG method and how WG can be applied to a model PDE problem invarious variational forms. In the authors' view, WG-FEM and HDG methods arebased on different philosophies and therefore represent different methodologiesin numerical PDEs, though they share something in common in their roots. Atheory and an example are given to show that the primal WG-FEM is notequivalent to the existing HDG [9].

The Basics of Weak Galerkin Finite Element Methods