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A quasi-nonlocal coupling method for nonlocal and local diffusion models

Publication ,  Journal Article
Du, Q; Li, XH; Lu, J; Tian, X
Published in: SIAM Journal on Numerical Analysis
January 1, 2018

In this paper, we extend the idea of “geometric reconstruction” to couple a nonlocal diffusion model directly with the classical local diffusion in one dimensional space. This new coupling framework removes interfacial inconsistency, ensures the flux balance, and satisfies energy conservation as well as the maximum principle, whereas none of existing coupling methods for nonlocal-to-local coupling satisfies all of these properties. We establish the well-posedness and provide the stability analysis of the coupling method. We investigate the difference to the local limiting problem in terms of the nonlocal interaction range. Furthermore, we propose a first order finite difference numerical discretization and perform several numerical tests to confirm the theoretical findings. In particular, we show that the resulting numerical result is free of artifacts near the boundary of the domain where a classical local boundary condition is used, together with a coupled fully nonlocal model in the interior of the domain.

Duke Scholars

Published In

SIAM Journal on Numerical Analysis

DOI

ISSN

0036-1429

Publication Date

January 1, 2018

Volume

56

Issue

3

Start / End Page

1386 / 1404

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Du, Q., Li, X. H., Lu, J., & Tian, X. (2018). A quasi-nonlocal coupling method for nonlocal and local diffusion models. SIAM Journal on Numerical Analysis, 56(3), 1386–1404. https://doi.org/10.1137/17M1124012
Du, Q., X. H. Li, J. Lu, and X. Tian. “A quasi-nonlocal coupling method for nonlocal and local diffusion models.” SIAM Journal on Numerical Analysis 56, no. 3 (January 1, 2018): 1386–1404. https://doi.org/10.1137/17M1124012.
Du Q, Li XH, Lu J, Tian X. A quasi-nonlocal coupling method for nonlocal and local diffusion models. SIAM Journal on Numerical Analysis. 2018 Jan 1;56(3):1386–404.
Du, Q., et al. “A quasi-nonlocal coupling method for nonlocal and local diffusion models.” SIAM Journal on Numerical Analysis, vol. 56, no. 3, Jan. 2018, pp. 1386–404. Scopus, doi:10.1137/17M1124012.
Du Q, Li XH, Lu J, Tian X. A quasi-nonlocal coupling method for nonlocal and local diffusion models. SIAM Journal on Numerical Analysis. 2018 Jan 1;56(3):1386–1404.

Published In

SIAM Journal on Numerical Analysis

DOI

ISSN

0036-1429

Publication Date

January 1, 2018

Volume

56

Issue

3

Start / End Page

1386 / 1404

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics