Stormer-Numerov HDG Methods for Acoustic Waves
Stormer-Numerov HDG Methods for Acoustic Waves
复制标题
DOI：
10.1007/s10915-017-0547-z
复制
发表时间：
2018-05
影响因子：
2.5
通讯作者：
Bernardo Cockburn;Zhixing Fu;Allan Hungria;L. Ji;M. Sánchez;F. Sayas
中科院分区：
文献类型：
--
作者：
Bernardo Cockburn;Zhixing Fu;Allan Hungria;L. Ji;M. Sánchez;F. Sayas
引入并分析了求解声波方程空间半离散化问题的第一能量守恒杂化不连续伽辽金方法。证明了半离散方法的最优收敛估计和超收敛估计。然后，我们引入了两步四阶时间Stormer-Numerov离散化，并证明了完全离散方法的能量守恒和收敛估计。特别地，我们证明了使用二阶多项式近似，可以得到四阶收敛性。数值实验验证了我们的理论收敛阶是尖锐的。我们还做了与同阶耗散法的比较实验。
We introduce and analyze the first energy-conservative hybridizable discontinuous Galerkin method for the semidiscretization in space of the acoustic wave equation. We prove optimal convergence and superconvergence estimates for the semidiscrete method. We then introduce a two-step fourth-order-in-time Stormer-Numerov discretization and prove energy conservation and convergence estimates for the fully discrete method. In particular, we show that by using polynomial approximations of degree two, convergence of order four is obtained. Numerical experiments verifying that our theoretical orders of convergence are sharp are presented. We also show experiments comparing the method with dissipative methods of the same order.