209 citations · 549 across the 39 of their papers we have counts for
5 papers · 1 filter
On a nonlocal Cahn-Hilliard model permitting sharp interfaces
Olena Burkovska, Max Gunzburger
A nonlocal Cahn-Hilliard model with a nonsmooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactio…
An energy-based coupling approach to nonlocal interface problems
Giacomo Capodaglio, Marta D'Elia, Pavel Bochev +1
Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations…
Peridynamics and Material Interfaces
Bacim Alali, Max Gunzburger
The convergence of a peridynamic model for solid mechanics inside heterogeneous media in the limit of vanishing nonlocality is analyzed. It is shown that the operator of linear per…
The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
Marta D'Elia, Max Gunzburger
We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several applications. In our analysis,…
Partial and spectral-viscosity models for geophysical flows
Qingshan Chen, Max Gunzburger, Xiaoming Wang
Two models based on the hydrostatic primitive equa- tions are proposed. The first model is the primitive equations with partial viscosity only, and is oriented towards large-scale…