A Nonoverlapping Domain Decomposition Method for an Exterior Anisotropic Quasilinear Elliptic Problem in Elongated Domains

Table 3

The relationship between 𝜃_𝑘 and convergence rate (𝑁=10, 𝑚=4, and 𝑀=16).

𝜃𝑘	𝑘	0	1	2	3	4	5	6	9
0.18	𝑒	4.4218𝐸−02	3.8978𝐸−02	3.6443𝐸−02	3.4711𝐸−02	3.3392𝐸−02	3.2341𝐸−02	3.1481𝐸−02	2.9668𝐸−02
	𝑒ℎ	—	5.2395𝐸−03	2.5350𝐸−03	1.7316𝐸−03	1.3185𝐸−03	1.0519𝐸−03	8.5974𝐸−04	5.0325𝐸−04
	𝑞ℎ	—	—	2.0668	1.4640	1.3133	1.2535	1.2235	1.1860
0.38	𝑒	4.4218𝐸−02	3.6741𝐸−02	3.3193𝐸−02	3.1073𝐸−02	2.9709𝐸−02	2.8795𝐸−02	2.8167𝐸−02	2.7174𝐸−02
	𝑒ℎ	—	7.4769𝐸−03	3.5473𝐸−03	2.1199𝐸−03	1.3646𝐸−03	9.1335𝐸−04	6.2830𝐸−04	2.3314𝐸−04
	𝑞ℎ	—	—	2.1078	1.6733	1.5535	1.4941	1.4537	1.3635
0.50	𝑒	4.4218𝐸−02	3.5398𝐸−02	3.1599𝐸−02	2.9601𝐸−02	2.8465𝐸−02	2.7784𝐸−02	2.7357𝐸−02	2.6751𝐸−02
	𝑒ℎ	—	8.8194𝐸−03	3.7989𝐸−03	1.9979𝐸−03	1.1359𝐸−04	6.8102𝐸−04	4.2741𝐸−04	1.3535𝐸−05
	𝑞ℎ	—	—	2.3216	1.9014	1.7588	1.6680	1.5934	1.4114
0.58	𝑒	4.4218𝐸−02	3.4503𝐸−02	3.0685𝐸−02	2.8865𝐸−02	2.7913𝐸−02	2.7377𝐸−02	2.7055𝐸−02	2.6609𝐸−02
	𝑒ℎ	−−−	9.7143𝐸−03	3.8180𝐸−03	1.8204𝐸−03	9.5190𝐸−04	5.3571𝐸−04	3.2246𝐸−04	9.9192𝐸−05
	𝑞ℎ	—	−−−	2.5443	2.0974	1.9124	1.7769	1.6613	1.4090
0.65	𝑒	4.4218𝐸−02	3.3720𝐸−02	2.9983𝐸−02	2.8358𝐸−02	2.7564𝐸−02	2.7135𝐸−02	2.6882𝐸−02	2.6530𝐸−02
	𝑒ℎ	—	1.0497𝐸−02	3.7371𝐸−03	1.6248𝐸−03	7.9382𝐸−04	4.2892𝐸−04	2.5372𝐸−04	7.9261𝐸−05
	𝑞ℎ	—	—	2.8089	2.3000	2.04687	1.8507	1.6905	1.3951