Name
Abstract | ||
|---|---|---|
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 nonlocalto-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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/17M1124012 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
nonlocal diffusion,quasi-nonlocal coupling,geometric reconstruction,modeling error estimate,well-posedness,physics preserving | Discretization,Boundary value problem,Energy conservation,Maximum principle,Coupling,Mathematical analysis,Finite difference,Diffusion (business),Mathematics,One-dimensional space | Journal |
Volume | Issue | ISSN |
56 | 3 | 0036-1429 |
Citations | PageRank | References |
1 | 0.37 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Qiang Du | 1 | 1692 | 188.27 |
| Xingjie Helen Li | 2 | 9 | 1.59 |
| Jianfeng Lu | 3 | 136 | 38.65 |
| Xiaochuan Tian | 4 | 14 | 3.01 |