Two-dimensional wave equation solved by generalized alternating flux based local discontinuous Galerkin method

Rong-Pei Zhang; Di Wang; Xi-Jun Yu; Xue-Bing Wen

doi:10.7498/aps.69.20190613

Journals >Acta Physica Sinica >Volume 69 >Issue 2 >Page 020202-1 > Article

Acta Physica Sinica
Vol. 69, Issue 2, 020202-1 (2020)

Two-dimensional wave equation solved by generalized alternating flux based local discontinuous Galerkin method

Rong-Pei Zhang¹, Di Wang¹, Xi-Jun Yu², and Xue-Bing Wen^1、*

Author Affiliations

¹College of Mathematics and Systems Science, Shenyang Normal University, Shenyang 110034, China

²Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

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DOI: 10.7498/aps.69.20190613 Cite this Article

Rong-Pei Zhang, Di Wang, Xi-Jun Yu, Xue-Bing Wen. Two-dimensional wave equation solved by generalized alternating flux based local discontinuous Galerkin method[J]. Acta Physica Sinica, 2020, 69(2): 020202-1 Copy Citation Text

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Fig. 1. (a) The triangulation mesh of Example 2; contour plot of solution at different time: (b) ; (c) ; (d) . (a)算例2的网格剖分和数值解在不同时刻(b) , (c) , (d) 时的波传播

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Fig. 2. Energy evolution with time for Example 2.算例2的能量随时间的演化

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Fig. 3. (a) The triangulation mesh of Example 3; contour plot of solution at different time: (b) ; (c) ; (d) . (a)算例3的网格剖分和数值解在不同时刻 (b) , (c) , (d) 时的波传播

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网格数	w的误差		p的误差
网格数	${L^2}$范数下误差	收敛阶	${L^2}$范数下误差	收敛阶
$8 \times 8$	2.80 × 10^–2	—	6.63× 10^–2	—
$16 \times 16$	5.75 × 10^–3	2.28	3.40× 10^–2	0.96
$32 \times 32$	1.64 × 10^–3	1.81	1.70× 10^–2	1.00
$64 \times 64$	4.62 × 10^–4	1.83	8.56× 10^–3	0.99
$128 \times 128$	9.20 × 10^–5	2.32	4.30 × 10^–3	0.99

Table 1. Error and convergence order of numerical solution and p. 数值解和p的误差和收敛阶数

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