A Seamless Local‐Nonlocal Coupling Diffusion Model With H ¹ Vanishing Nonlocality Convergence

Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local‐nonlocal coupling diffusion model in this paper. In our model, a finite constant interaction horizon is equipped in the nonlocal part and transmission conditions are imposed on a co‐dimension one interface. To achieve a seamless coupling, we introduce an auxiliary function to merge the nonlocal model with the local part and design a proper coupling transmission condition to ensure the stability and convergence. In addition, by introducing bilinear form, well‐posedness of the proposed model can be proved and convergence to a standard elliptic transmission model with first order in norm can be derived.