Journal
ADVANCES IN CALCULUS OF VARIATIONS
Volume -, Issue -, Pages -Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/acv-2023-0028
Keywords
Nonlocal gradients; peridynamics; fractional Sobolev spaces; discrete approximations; discrete-to-continuum convergence
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This paper focuses on the discrete approximation of functionals depending on nonlocal gradients, and proves that the discretized functionals are coercive in classical Sobolev spaces.
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.
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