A method is developed to model continuum (finite element) and discrete [kinetic Monte Carlo (kMC)] diffusion occurring simultaneously in connected regions of space. The two regions are coupled across ail interface using ail iterative domain-decomposition approach ill which time-dependent boundary conditions are applied oil the kMC region (concentration) and oil the continuum region (flux). Evolving forward in small time increments permits iterations in the kMC region to be performed only in a narrow band near the interface. An on-the-fly convergence criterion based oil the inherent fluctuations ill the discrete problem is developed, Application to the decay of a Gaussian concentration profile demonstrates the accuracy and efficiency of the method. Generalizations to more complex problems in two and three dimensions, and with spatially varying diffusivity due to interactions or applied stress fields, are straightforward.