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arXiv · 1607.03940

Quasinonlocal coupling of nonlocal diffusions

Xingjie Helen Li·Jianfeng Lu
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Abstract

We developed a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method for crystalline solids. The proposed coupling model is coercive with respect to the energy norms induced by the nonlocal diffusion kernels as well as the $L^2$ norm, and it satisfies the maximum principle. A finite difference approximation is used to discretize the coupled system, which inherits the property from the continuous formulation. Furthermore, we design a numerical example which shows the discrepancy between the fully nonlocal and fully local diffusions, whereas the result of the coupled diffusion agrees with that of the fully nonlocal diffusion.

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Xingjie Helen Li, Jianfeng Lu. 2016-07-13. Quasinonlocal coupling of nonlocal diffusions. https://arxiv.org/abs/1607.03940

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