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. Author manuscript; available in PMC: 2012 Jan 20.
Published in final edited form as: J Comput Phys. 2011 Jan 20;230(2):375–393. doi: 10.1016/j.jcp.2010.09.020

Table 1.

Error in L2 norm and convergence rate for the fluid velocities and the surfactant concentrations.

Grid ‖u − uref‖2
(×10−2)		 Rate ‖v − vref‖2
(×10−1)		 Rate
1/16 4.03 - 8.49 -
1/32 1.84 1.13 5.20 0.71
1/64 0.503 1.87 1.57 1.73
1/128 0.0754 2.74 0.203 2.95
‖f − fref‖2
(×10−1)		 Rate ‖F − Fref‖2
(×10−1)		 Rate
1/16 2.93 - 5.96 -
1/32 2.23 0.39 3.64 0.71
1/64 1.58 0.50 1.19 0.92
1/128 0.686 1.20 0.834 1.20