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Theory and Modern Applications

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

Ï€/10

Ï€/20

Ï€/30

Ï€/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