A Nitsche mixed extended finite element method for the biharmonic interface problem

Abstract

In this paper, a Nitsche mixed extended finite element method based on Ciarlet–Raviart formulation is proposed to discretize the biharmonic interface problem with interface unfitted meshes. We present a discrete mixed approximate formulation based on the piecewise quadratic continuous finite element space. By adding a stabilization procedure, we get the discrete inf–sup condition and prove a suboptimal a priori error estimate for the discrete problem. If the solution of the dual problem satisfies the additional regularity condition, then an optimal a priori error estimate for stream variable under piecewise H1-norm is obtained. It is shown that all results are uniform with respect to the mesh size, and the location of the interface relative to the mesh. Finally, numerical experiments are carried out to demonstrate our theoretical results.