An energy-based coupling approach to nonlocal interface problems

2020/01/11 by Capodaglio, Giacomo, D'Elia, Marta, Bochev, Pavel +1 · 1 citation
#34b10 #35j50 #45a05 #74a50 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2001.03696

Abstract

Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations fail to capture effects caused by long-range forces at the microscale and mesoscale. However, the application of nonlocal models to problems involving interfaces such as multimaterial simulations and fluid-structure interaction, is hampered by the lack of a rigorous nonlocal interface theory needed to support numerical developments. In this paper, we use an energy-based approach to develop a mathematically rigorous nonlocal interface theory which provides a physically consistent extension of the classical perfect interface PDE formulation. Numerical examples validate the proposed framework and demonstrate the scope of our theory.

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• An asymptotically compatible unfitted finite element methods for nonlocal elliptic Interfaces: local limits and sharp error estimates

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