Continuous and discontinuous finite element methods for a peridynamics model of mechanics

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Peridynamic Theory of Solid Mechanics (2010, methodology): “A finite element formulation was also developed by Chen and Gunzburger [14], who consider the one dimensional equations for a finite bar.”
Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems (2013, background): “Nonlocal diffusion problems such as (2) have been analyzed in the recent works [2, 21, 22, 28], and techniques for an accurate numerical solution have been developed and applied to diverse applications [18, 3, 16, 17, 35, 38, 41].”
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints (2012, background): “We again observe that if s ∈ (0, 1/2), the error and condition number estimates also hold for discontinuous Galerkin approximations, because in this case all piecewise polynomial spaces with respect to the triangulation, whether globally continuous or not, are conforming for the internal discretizat”