Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes
Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes
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权重调整的不连续伽辽金方法：曲线网格
DOI：
10.1137/16m1089198
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
T. Warburton
中科院分区：
文献类型：
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作者：
Jesse Chan;Russell J. Hewett;T. Warburton
传统时域不连续伽辽金（DG）方法由于存储密集元素矩阵，导致高阶近似时存储成本较高。在这项工作中，我们提出了一种用于曲线网格的权重调整 DG (WADG) 方法，该方法可以降低存储成本，同时保持能量稳定性。先验误差估计表明，在网格上的足够条件下，可以保持高阶精度，这可以通过不同网格序列的收敛测试来说明。数值和计算实验验证了 WADG 对于弯曲域模型问题的准确性和性能。
Traditional time-domain discontinuous Galerkin (DG) methods result in large storage costs at high orders of approximation due to the storage of dense elemental matrices. In this work, we propose a weight-adjusted DG (WADG) methods for curvilinear meshes which reduce storage costs while retaining energy stability. A priori error estimates show that high order accuracy is preserved under sufficient conditions on the mesh, which are illustrated through convergence tests with different sequences of meshes. Numerical and computational experiments verify the accuracy and performance of WADG for a model problem on curved domains.