209 citations · 549 across the 39 of their papers we have counts for
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A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions
Giacomo Capodaglio, Marta D'Elia, Max Gunzburger +3
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a…
A cookbook for finite element methods for nonlocal problems, including quadrature rules and approximate Euclidean balls
Marta D'Elia, Max Gunzburger, Christian Vollmann
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) s…
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…
Numerical methods for nonlocal and fractional models
Marta D'Elia, Qiang Du, Christian Glusa +3
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swa…
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…