A high-order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface is allowed to cut through the background mesh. To avoid problems with small cuts, stabilizing terms are added to the bilinear forms corresponding to the mass and stiffness matrix. The stabilizing terms penalize jumps in normal derivatives over the faces of the elements cut by the boundary/interface. This ensures a stable discretization independently of how the boundary/interface cuts the mesh. Nitsche’s method is used to enforce boundary and interface conditions, resulting in symmetric bilinear forms. As a result of the symmetry, an energy estimate can be made and optimal order a priori error estimates are derived for the single domain problem. Finally, numerical experiments in two dimensions are presented that verify the order of accuracy and stability with respect to small cuts.

中文翻译：

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弹性波方程的高阶有限元

提出了求解弹性波动方程的高阶有限元方法。既解决了单个域问题又解决了接口问题。边界或界面可以穿过背景网格。为避免小切口的问题，将稳定项添加到与质量和刚度矩阵相对应的双线性形式中。稳定项会惩罚正态导数在边界/界面所切割元素的表面上的跳跃。这样可以确保稳定的离散度，而与边界/界面如何切割网格无关。Nitsche的方法用于强制边界和界面条件，从而产生对称的双线性形式。作为对称性的结果，可以进行能量估计并且针对单域问题导出先验误差估计的最佳阶数。最后，