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. Author manuscript; available in PMC: 2011 Jun 1.

Published in final edited form as: J Comput Phys. 2011 Jun;230(13):5239–5262. doi: 10.1016/j.jcp.2011.03.020

Table 1.

Numerical errors and orders in solving PNP equations for the spherical test case.

		Boundary condition I				Boundary condition II

	mesh size	L_∞	L_∞ order	L₂	L₂ order	L_∞	L_∞ order	L₂	L₂ order

	h = 0.2	3.17E-3	—	2.84E-4	—	3.34E-3	—	2.86E-4	—
Φ	h = 0.1	8.32E-4	1.93	7.41E-5	1.94	8.49E-4	1.98	7.52E-5	1.93
	h = 0.05	2.23E-4	1.90	2.02E-5	1.88	2.15E-4	1.98	1.91E-5	1.98

	h = 0.2	5.63E-3	—	1.80E-3	—	3.08E-3	—	9.27E-4	—
C₁	h = 0.1	1.32E-3	2.09	4.32E-4	2.06	7.70E-4	2.00	2.35E-4	1.98
	h = 0.05	3.00E-4	2.14	9.49E-5	2.19	1.90E-4	2.02	5.92E-5	1.99

	h = 0.2	3.77E-3	—	1.22E-3	—	1.73E-3	—	5.08E-4	—
C₂	h = 0.1	1.09E-3	1.79	3.32E-4	1.88	4.32E-4	2.00	1.29E-4	1.98
	h = 0.05	3.38E-4	1.84	9.23E-5	1.85	1.11E-4	1.96	3.27E-5	1.98