An Asymptotically Compatible Coupling Formulation for Nonlocal Interface Problems with Jumps

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