Genaralized FE Methods

GFEM - Generalized Finite Element Methods

The generalized finite element method (GFEM) was first introduced in [Melenk95] and [Babuska96]. It combines desirable features of the standard finite element method and meshless methods.

The key difference of the GFEM compared to the traditional FEM is the construction of the ansatz space. Each node of the finite element mesh carries a number of ansatz functions, expressed in terms of the global coordinate system. Those ansatz functions are multiplied by a partition of unity and serve as element ansatz functions in the patch constituted by the elements incident at the node.

Using this technique to create the ansatz space allows for arbitrary ansatz functions. C0-continuity is enforced by construction.

[Melenk95] J. M. Melenk, On generalized finite element methods, Ph.D. dissertation, University of Maryland, College Park, MD, (1995)
[Babuska96] I. Babuska, J. M. Melenk, The partition of unity finite element method: Basic theory and applications, Comp. Meth. Appl. Mech. Engrg., 139, (1996), 289--314