We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible discontinuous Galerkin methods on unstructured grids by a penalty based technique. At the interface between the two methods, we construct projection operators for the pointwise finite difference solutions and discontinuous Galerkin solutions based on piecewise polynomials. In addition, we optimize the projection operators for both accuracy and spectrum. We prove that the overall discretization conserves a discrete energy, and verify optimal convergence in numerical experiments.

翻译：我们提出了一种用于求解二阶形式弹性波方程的高阶精确数值方法。该方法通过基于罚函数的技术，将计算高效的笛卡尔网格有限差分格式与在非结构网格上具有几何灵活性的间断伽辽金方法进行混合。在两种方法的交界面处，我们基于分段多项式构造了针对点态有限差分解和间断伽辽金解的投影算子。此外，我们对投影算子进行了精度和频谱优化。我们证明了整体离散格式能够守恒离散能量，并通过数值实验验证了其最优收敛性。