Two-Level Brezzi-Pitkäranta Discretization Method Based on Newton Iteration for Navier-Stokes Equations with Friction Boundary Conditions

Table 2

Convergence of two-level Newton iteration scheme.

1/𝐻	1/ℎ	‖𝐮−𝐮^ℎ‖‖𝐮‖	Rate	‖𝐮−𝐮^ℎ‖𝑉‖𝐮‖𝑉	Rate	‖𝑝−𝑝^ℎ‖‖𝑝‖	Rate	CPU (s)
4	4^2	2.52556𝑒−02	/	1.77813𝑒−01	/	1.11990𝑒−02	/	0.414
6	6^2	4.30902𝑒−03	2.1806	7.17049𝑒−02	1.1199	5.03215𝑒−03	0.9865	1.522
8	8^2	1.23630𝑒−03	2.1701	3.83421𝑒−02	1.0880	2.44665𝑒−03	1.2533	4.553
10	10^2	4.79543𝑒−04	2.1221	2.39285𝑒−02	1.0564	1.32261𝑒−03	1.3783	11.493
12	12^2	2.25836𝑒−04	2.0651	1.63919𝑒−02	1.0374	7.82669𝑒−04	1.4388	25.997
14	14^2	1.21790𝑒−04	2.0029	1.19445𝑒−02	1.0266	4.98560𝑒−04	1.4628	45.606
16	16^2	7.27796𝑒−05	1.9279	9.09620𝑒−03	1.0200	3.36415𝑒−04	1.4730	77.029
18	18^2	4.72790𝑒−04	1.8312	7.16069𝑒−03	1.0156	2.37461𝑒−04	1.4787	129.046