A Nitsche extended finite element method for the biharmonic interface problem

Abstract In this paper, a Nitsche extended finite element method is presented to discretize the biharmonic interface problem with unfitted meshes. A new interface condition is proposed for the biharmonic interface problem, and the construction of the finite element space is based on the so-called modified Morley finite element for the interface elements and the Morley finite element for the others. By adding a stabilization procedure, we obtain the well-posedness for the discrete problem and prove an optimal a priori error estimate in the energy norm. It is shown that all results are uniform with respect to the mesh size, the material parameter quotient, and the position of the interface. Finally, numerical experiments are carried out to verify theoretical results.