Quasi-nonlocal coupling of nonlocal diffusions

Published

Journal Article

© 2017 Society for Industrial and Applied Mathematics. We developed a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasi-nonlocal 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 L2 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 that 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.

Full Text

Duke Authors

Cited Authors

  • Li, XH; Lu, J

Published Date

  • January 1, 2017

Published In

Volume / Issue

  • 55 / 5

Start / End Page

  • 2394 - 2415

International Standard Serial Number (ISSN)

  • 0036-1429

Digital Object Identifier (DOI)

  • 10.1137/16M1086443

Citation Source

  • Scopus