Chinese Journal of Mechanical Engineering

Table 7 Errors and orders of convergence on the different cell with the Neumann boundary

From: New Immersed Boundary Method on the Adaptive Cartesian Grid Applied to the Local Discontinuous Galerkin Method

i	q ₁				u
i	L^∞	Order	L²	Order	L^∞	Order	L²	Order
1	1.25 × 10⁻⁴		1.25 × 10⁻⁴		8.65 × 10⁻³		7.06 × 10⁻⁴
2	3.59 × 10⁻⁴	− 4.33	6.72 × 10⁻⁵	2.48	5.32 × 10⁻³	1.99	3.56 × 10⁻⁴	3.05
3	5.80 × 10⁻⁵	9.60	4.51 × 10⁻⁵	2.10	5.22 × 10⁻³	0.10	2.83 × 10⁻⁴	1.20
4	4.51 × 10⁻⁵	1.66	3.22 × 10⁻⁵	2.23	5.70 × 10⁻³	− 0.57	2.33 × 10⁻⁴	1.26
5	2.92 × 10⁻⁵	2.99	2.48 × 10⁻⁵	1.79	5.30 × 10⁻³	0.50	1.86 × 10⁻⁴	1.58
6	2.77 × 10⁻⁷	28.21	1.59 × 10⁻⁵	2.69	3.23 × 10⁻³	3.00	1.11 × 10⁻⁴	3.10

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