A linear triangular finite element method-implicit difference scheme (FEM-IDS) for the solution of second order strongly damped wave equation (SDWE) with memory on domain with interfaces is proposed. Sufficient conditions that guarantee the existence of a unique solution are given. The finite element discretization is such that the arbitrary (but smooth) interface is first approximated by a polygon with a boundary whose vertices all lie on the interface. With the interface being at $\sigma$-distance from the approximate interface, linear interpolation operator incorporating the influence of $\sigma$ isproved. This together with Ritz–Volterra operator and some auxiliary error estimates in the neighborhood of the interface are used to obtain the convergence estimate of the proposed scheme. The scheme is applied to some test examples and the numerical results confirm the computational efficiency of the method.

提出了一种线性三阶有限元隐式差分格式（FEM-IDS），用于求解带界面域记忆的二阶强阻尼波动方程（SDWE）。给出了保证存在唯一解决方案的充分条件。有限元离散化使得任意（但平滑）界面首先由具有边界的多边形逼近，该边界的顶点全部位于该界面上。界面位于$\sigma$-距近似接口的距离，线性插值算子合并了 $\sigma$被证明。这与Ritz-Volterra算子以及接口附近的一些辅助误差估计一起用于获得所提出方案的收敛估计。该方案被应用于一些测试实例，数值结果证实了该方法的计算效率。