Discretization error estimates for discontinuous Galerkin isogeometric analysis

Figures & data

Figure 1. Discretization errors for splines of maximum smoothness as function in ℓ.

Figure 2. Discretization errors for splines of maximum smoothness as function in p.

Table 1. Discretization errors in case of maximum smoothness.

	p = 2			p = 3		p = 4		p = 5
ℓ	dofs	$e_{\ell ,p}$	$r_{\ell ,p}$	$e_{\ell ,p}$	$r_{\ell ,p}$	$e_{\ell ,p}$	$r_{\ell ,p}$	dofs	$e_{\ell ,p}$	$r_{\ell ,p}$
2	911	0.7115		0.6170		0.5513		1757	0.5104
3	2855	0.3651	1.9	0.3375	1.8	0.2736	2.0	4229	0.2669	1.9
4	10007	0.0650	5.6	0.0246	13.7	0.0096	28.5	12437	0.0037	72.0
5	37028	0.0112	5.8	0.0016	15.1	2.6e−4	36.3	41909	4.4e−5	84.1
6	144311	0.0026	4.3	1.8e−4	9.3	1.3e−5	20.3	153077	9.8e−7	44.9
7	567095	6.4e−4	4.1	2.1e−5	8.3	7.6e−7	17.1	584309	2.8e−8	35.4
Expected:			4		8		16			32

Figure 3. Discretization errors for splines of minimum smoothness as function in ℓ.

Table 2. Discretization errors in case of minimum smoothness.

	p = 2			p = 3		p = 4		p = 5
ℓ	dofs	$e_{\ell ,p}$	$r_{\ell ,p}$	$e_{\ell ,p}$	$r_{\ell ,p}$	$e_{\ell ,p}$	$r_{\ell ,p}$	dofs	$e_{\ell ,p}$	$r_{\ell ,p}$
2	2788	0.4242		0.2292		0.1087		14980	0.0408
3	10724	0.1439	1.9	0.0424	5.4	0.0094	11.6	58916	0.0018	22.7
4	42052	0.0398	5.6	0.0057	7.7	6.5e−4	14.5	233668	6.0e−5	30.2
5	166532	0.0101	5.8	7.3e−4	7.8	4.1e−5	15.7	930692	1.9e−6	31.5
6	662788	0.0025	4.3	9.2e−5	8.0	2.6e−6	15.9	3714820	5.9e−8	31.9
7	2644484	6.4e−4	4.1	1.1e−5	8.0	OoM		14843396	OoM
Expected:			4		8		16			32

Figure 4. Errors for splines of maximum smoothness with $4^{\iota }$ patches and $\ell =7-\iota$.

Table 3. Discretization errors in case of maximum smoothness in 3D.

	p = 2			p = 3		p = 4		p = 5
ℓ	dofs	$e_{\ell ,p}$	$r_{\ell ,p}$	$e_{\ell ,p}$	$r_{\ell ,p}$	$e_{\ell ,p}$	$r_{\ell ,p}$	dofs	$e_{\ell ,p}$	$r_{\ell ,p}$
0	33	1.0210		1.0180		0.8095		456	0.3298
1	100	0.8180	1.2	0.8530	1.2	0.1746	4.6	793	0.2096	1.6
2	456	0.3623	2.3	0.2310	3.7	0.0602	2.9	1905	0.0415	5.0
3	2728	0.0558	6.5	0.0117	19.7	0.0029	21.1	6553	6.1e−4	68.6
4	18888	0.0118	4.7	0.0011	10.8	1.1e−4	25.5	30921	1.1e−5	55.1
Expected:			4		8		16			32