Splitting methods and numerical approximations for a coupled local/nonlocal diffusion model

In this paper, we study a splitting approach and a numerical method to approximate solutions to an evolution problem that couples local and nonlocal diffusion operators. The method proposed here takes advantage of the fact that we can show a splitting structure for our evolution equation allowing us to deal with the local and nonlocal parts of the equation separately. This has the capability of being quite flexible, allowing, for example, to consider different meshes in the local and in the nonlocal region. We prove convergence of the method and include some numerical experiments that show some qualitative features of the model.