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The extension of the VGFEM framework on tetrahedral elements is not straightforward since (i) definition of the PU function on an arbitrary polyhedra is difficult, and (ii) one needs to carefully handle the coupling of FEM and VGFEM basis functions. This paper presents the means through which these difficulties can be overcome. The rest of the paper is organized as follows: in the next section, we present the framework of VGFEM with tetrahedral elements, and then explain the hybrid FEM-VGFEM technique. The new VGFEM framework is validated via a a set of simulations. Finally, conclusions and the future research are presented in the last section.