Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method

We extend the classical Nitsche type weak boundary conditions to a fictitious domain setting. An additional penalty term, acting on the jumps of the gradients over element faces in the interface zone, is added to ensure that the conditioning of the matrix is independent of how the boundary cuts the mesh. Optimal a priori error estimates in the H1 and L2 norms are proved as well as an upper bound on the condition number of the system matrix.