中文摘要：

本义研究黏性流体与零厚度弹性材料界面上的耦合运动问题．利用沉浸边界法与时间步长法，半Lagrange离散法，对速度分解后的Stokes部分与正则部分进行求解，获得了关于耦合运动中二阶PDE求解的一般方法，推广了文献[14，15，18]的结果．

英文摘要：

This paper investigates the coupled motion of a viscous fluid and an elastic material interface with zero thickness. By using the immersed interface method and time-stepping method, semi-Lagrange discrete method respectively, the decomposed Stokes part and regular part are solved, and the general calculating method of the second-order PDE related to the coupled motion is obtained. Furthermore, we improve the results of [14, 15, 18 ].