Local discontinuous Galerkin methods for the carpet cloak model
Local discontinuous Galerkin methods for the carpet cloak model
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DOI：
10.4310/amsa.2022.v7.n1.a4
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发表时间：
2022
影响因子：
0.6
通讯作者：
Xinyue Yu;Jichun Li;Chi-Wang Shu
中科院分区：
文献类型：
--
作者：
Xinyue Yu;Jichun Li;Chi-Wang Shu
。 DG 方法在[32]中的地毯斗篷模型数值模拟中已被证明具有良好的性能。然而，稳定性分析和误差估计还有待完成。在本文中，我们介绍了蛙式 DG 方法来求解地毯斗篷模型。我们证明了半离散方案的稳定性、非结构化网格的次优误差估计以及张量积网格的最优误差估计。然后给出了全离散方案并证明了其稳定性。最后，分别给出了矩形和三角形网格的数值精度测试，并给出了采用DG方案对地毯斗篷模型中波传播的数值模拟结果。
. The DG methods have been shown to have good performance in numerical simulations of the carpet cloak model in [32]. However, the stability analysis and the error estimate are left to be done. In this paper, we introduce the leap-frog DG methods to solve the carpet cloak model. We prove the stability of the semi-discrete scheme, the sub-optimal error estimate for unstructured meshes, and the optimal error estimate for tensor-product meshes. Then, the fully discrete scheme is stated and the stability is proved. Finally, the numerical accuracy tests on rectangular and triangular meshes are given respectively, and the results of numerical simulations of the wave propagation in the carpet cloak model using the DG scheme are presented.