Numerical Integration of Some Arbitrary Functions over an Ellipsoid by Discretizing into Hexahedral Elements for Biomaterial Studies

Table 6

Integral results of cubic tetrahedral elements: comparison with GGQ and GQ.

Sl. No	Functions	Exact value	20 N	GGQ (N = 5)	N = 10	N = 15	N = 20
1		2.3561	2.3897	2.3627	2.3632	2.3632	2.3566
				N = 4	N = 6	N = 8	N = 10
				2.3563	2.3562	2.3561	2.3561
2	1	3.1415	3.1383	3.1315
				N = 4	N = 6	N = 8	N = 10
				3.1315	3.1415	3.1415	3.1415
3		0.7500	0.7614	0.7500
				N = 4	N = 6	N = 8	N = 10
				0.7500	0.7500	0.7500	0.7500
4		0.6857	0.6914	0.6866
				N = 4	N = 6	N = 8	N = 10
				0.6861	0.6859	0.6857	0.6857
5		NInt = 4.6396	4.6108	4.6108
				N = 4	N = 6	N = 8	N = 10
				4.6108	4.6108	4.6108	4.6108
6		NInt = 2.2146	2.2008	2.2008
				N = 4	N = 6	N = 8	N = 10
				2.2005	2.2007	2.2000	2.2008
7		3.2313	3.2773	3.2315
				N = 4	N = 6	N = 8	N = 10
				3.2373	3.2313	3.2313	3.2313
8		0.0580	0.0578	0.0581
				N = 4	N = 6	N = 8	N = 10
				0.0583	0.0580	0.0580	0.0580
9		Singularity and highly oscillatory function		1.9206
				N = 4	N = 6	N = 8	N = 10
				1.9211	1.9261	1.9261	1.9261
10		2.2884	2.2894	2.2884
				N = 4	N = 6	N = 8	N = 10
				2.2956	2.2885	2.2884	2.2884
11		2.5132		2.5132
				N = 4	N = 6	N = 8	N = 10
				2.4987	2.5138	2.5132	2.5132