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.

本文提出了一种Nitsche扩展有限元方法来离散化带有不拟合网格的双调和界面问题。为双调和界面问题提出了一个新的界面条件，有限元空间的构造基于界面元的所谓改进的Morley有限元和其他元素的Morley有限元。通过添加稳定程序，我们获得了离散问题的适定性，并证明了能量范数中的最优先验误差估计。结果表明，所有结果在网格大小，材料参数商和界面位置方面都是一致的。最后，进行了数值实验以验证理论结果。