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

An asymptotically compatible coupling formulation for nonlocal interface problems with jumps