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Table 4 The space order of convergence and mass errors of the scheme for \(u_{0}(x)= \cos 4 x\)

From: A mass-conserved domain decomposition method for the unsaturated soil flow water problem

t h π/10 π/20 π/30 π/40
0.01 \(L^{2}\)-norm- 5.6678E−2 1.3473E−2 5.9676E−3 3.3558E−3
order 2.0726 2.0085 2.0010
mass error 6.7035E−15 4.1767E−15 5.6799E−18 1.5305E−15
0.2 \(L^{2}\)-norm- 6.8241E−2 1.5387E−2 6.7852E−3 3.8226E−3
order 2.1489 2.0194 1.9946
mass error 7.9878E−15 2.4906E−15 2.2245E−15 1.8313E−15
0.5 \(L^{2}\)-norm- 5.4733E−2 1.3158E−2 5.8475E−3 3.3109E−3
order 2.0565 2.0002 1.9772
mass error 8.4530E−15 9.1308E−15 4.9728E−15 1.7777E−15