Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface

The objective of this work is to study a diffusion equation with non-standard transmission conditions, which include discontinuities and Ventcel boundary conditions at the interface. In order to handle jumps and means of the flux and the test-functions, we use broken Sobolev spaces. We present a Nitsche type finite element approach and compare it with a discontinuous Galerkin method. We establish consistency, stability and a priori error estimates, and verify them numerically.