Discrete approximation of nonlocal-gradient energies
We study a discrete approximation of functionals depending on nonlocal gradients. The discretized functionals are proved to be coercive in classical Sobolev spaces. The key ingredient in the proof is a formulation in terms of circulant Toeplitz matrices.
nonlocal gradients, peridynamics, fractional Sobolev spaces, discrete approximations, discrete-to-continuum convergence