Nitsche-type finite element method for elliptic problems with singularities

Abstract

The paper deals with a Nitsche-type finite element method for treating non-matching meshes at the interface of a domain decomposition. This method is applied to transmission (or interface) problems with discontinuous coefficients, where the polygonal boundary of the plane domain and the polygonal interface cause singularities in the solution. 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 Nitsche-type finite element scheme and error estimates are given when the solution has a low degree of regularity. For appropriate local mesh refinement, optimal convergence rates as known for the classical finite element method and regular solution are obtained. Numerical tests illustrate the approach and confirm the theoretical results.