AN ASYMPTOTICALLY COMPATIBLE COUPLING FORMULATION FOR NONLOCAL INTERFACE PROBLEMS WITH JUMPS

We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the well-posedness of the weak form, we demonstrate that solutions to the nonlocal interface problem converge to the corresponding local counterpart when the nonlocal data are appropriately prescribed. Several numerical tests in one and two dimensions show the applicability of our technique, its numerical convergence to exact nonlocal solutions, its convergence to the local limit when the horizons vanish, and its robustness with respect to the patch test.

Automated summary

This study presents a mathematically rigorous formulation for a nonlocal interface problem with jumps, and proposes an asymptotically compatible finite element discretization for the weak form of the interface problem. Numerical tests demonstrate the applicability, numerical convergence to exact nonlocal solutions, convergence to the local limit, and robustness with respect to the patch test of the technique.