论文标题
有限的差异 - 二阶形式的波程
A finite difference - discontinuous Galerkin method for the wave equation in second order form
论文作者
论文摘要
我们基于高阶准确的有限差异方法和不连续的Galerkin方法，以二阶形式为波方程开发了一个混合空间离散化。杂交结合了笛卡尔网格上有限差异方法的计算效率，以及在非结构化网格上不连续的盖尔金方法的几何灵活性。这两个空间离散是通过界面处的惩罚技术结合的，因此总体半差异可以满足离散的能量估计，以确保稳定性。此外，最佳收敛是从某种意义上获得的，即使用三阶局部多项式将第四阶有限差异方法与不连续的盖尔金方法相结合时，总体收敛速率为第四阶。此外，我们使用一种新颖的方法来通过结合能量方法和相应的一个维模型问题的能量方法和正常模式分析来得出半差异的误差估计。在数值实验中验证了稳定性和准确性分析。
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite difference methods on Cartesian grids and geometrical flexibility of discontinuous Galerkin methods on unstructured meshes. The two spatial discretizations are coupled by a penalty technique at the interface such that the overall semidiscretization satisfies a discrete energy estimate to ensure stability. In addition, optimal convergence is obtained in the sense that when combining a fourth order finite difference method with a discontinuous Galerkin method using third order local polynomials, the overall convergence rate is fourth order. Furthermore, we use a novel approach to derive an error estimate for the semidiscretization by combining the energy method and the normal mode analysis for a corresponding one dimensional model problem. The stability and accuracy analysis are verified in numerical experiments.
