A fitted space-time finite element method for an advection-diffusion problem with moving interfaces

This paper presents a fitted space-time finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the spatial gradient of solution across the interface. We use the Banach-Necas-Babuska theorem to show the well-posedness of the continuous variational problem. A fully discrete finite-element based scheme is analyzed using the Galerkin method and unstructured fitted meshes. An optimal error estimate is established in a discrete energy norm under appropriate globally low but locally high regularity conditions. Some numerical results corroborate our theoretical results.