On a family of discontinuous Galerkin fully-discrete schemes for the wave equation
On a family of discontinuous Galerkin fully-discrete schemes for the wave equation
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DOI：
10.1007/s40314-021-01423-8
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发表时间：
2021-02
影响因子：
2.6
通讯作者：
Limin He;W. Han;Fei Wang
中科院分区：
文献类型：
--
作者：
Limin He;W. Han;Fei Wang
本文研究了一类求解二阶波动方程的间断Galerkin（DG）全离散格式。空间变量离散化是基于DG方法的应用。时间变量离散化依赖于参数。在适当的正则性假设下，给出了无条件地关于空间网格尺寸和时间步长的数值格式以及满足关于网格尺寸和时间步长的Courant-Friedrichs-Lewy稳定性条件的数值格式的最优阶误差界.最佳阶误差估计的导出和范数。仿真结果提供了理论预测的最佳收敛阶数的数值证据。
In this paper, we study a family of discontinuous Galerkin (DG) fully discrete schemes for solving the second-order wave equation. The spatial variable discretization is based on an application of the DG method. The temporal variable discretization depends on a parameter. Under suitable regularity hypotheses on the solution, optimal order error bounds are shown for the numerical schemes with, unconditionally with respect to the spatial mesh-size and the time-step, and for the numerical schemes withwhere a Courant–Friedrichs–Lewy stability condition is satisfied relating the mesh-size and the time-step. The optimal order error estimates are derived forandnorms. Simulation results are reported to provide numerical evidence of the optimal convergence orders predicted by the theory.