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Theory and Modern Applications

Table 8 Errors of numerical solutions using \(h_{x}=h_{y}=0.01\) with different Pe

From: A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations

 

Method

Average error

\(L^{2}\) norm error

\(L^{\infty }\) norm error

Pe = 100

t = 0.01

DHOC-ADI

8.05924 × 10−5

2.75150 × 10−4

2.32611 × 10−3

τ = 2.5 × 10−5

HOC-ADI

1.25123 × 10−3

4.37851 × 10−3

4.70167 × 10−2

EHOC-ADI

2.01865 × 10−4

7.43597 × 10−4

8.83915 × 10−3

RHOC-ADI

9.64574 × 10−5

3.54495 × 10−4

3.20386 × 10−3

Pe = 1000

t = 0.001

DHOC-ADI

8.06267 × 10−5

2.79187 × 10−4

2.32880 × 10−3

τ = 2.5 × 10−6

HOC-ADI

1.45299 × 10−3

5.31763 × 10−3

4.90389 × 10−2

EHOC-ADI

2.16272 × 10−4

8.09967 × 10−4

9.79204 × 10−3

RHOC-ADI

1.01878 × 10−4

3.81345 × 10−4

3.51572 × 10−3

Pe = 10,000

    

t = 0.0001

DHOC-ADI

8.09330 × 10−5

2.80772 × 10−4

2.33917 × 10−3

τ = 2.5 × 10−7

HOC-ADI

1.46509 × 10−3

5.38039 × 10−3

4.89280 × 10−2

EHOC-ADI

2.17773 × 10−4

8.16985 × 10−4

9.89365 × 10−3

RHOC-ADI

1.02455 × 10−4

3.84194 × 10−4

3.54963 × 10−3