The Nitsche mortar finite‐element method for transmission problems with singularities

The paper deals with a Nitsche‐type finite‐element method for treating non‐matching meshes at the interface of some domain decomposition. The method is extended to transmission (or interface) problems of the plane with Dirichlet boundary conditions entailing singularities at the corners or endpoints of the polygonal interface. In a natural way, the interface of the transmission problem is taken as the interface of the domain decomposition and of the non‐matching meshes. Properties of the finite‐element scheme and error estimates are proved. For appropriate local mesh refinement, optimal convergence rates as known for the classical finite‐element method and regular solution are derived. Some numerical tests illustrate the approach and confirm the theoretical results.