In this paper we review some basic notions of partition of unity-based discontinuous finite elements showing their relation to the Generalized Finite Element Method. A minimal one-dimensional example illustrates some of the issues related to the computer implementation of the method and highlights the relative simplicity of the approach. The ability of the approach in describing displacement discontinuities independently of the finite element mesh is shown in a classical crack propagation problem in an elastic medium. We also illustrate some limitations of this method when used in conjunction with the dummy stiffness approach.
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