Theory and Modern Applications
Table 4 The error norms of numerical solutions and the rate of convergence in space where \(\tau =2.5\times 10^{-6}\)
From: A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations
\(h_{x}=h_{y}\) | \(L^{2} \) error norm | Rate | \(L^{\infty }\) error norm | Rate | |
|---|---|---|---|---|---|
DHOC-ADI | 0.2 | 2.47422 × 10−2 | – | 6.68806 × 10−2 | – |
0.1 | 2.02976 × 10−3 | 3.60759 | 9.10817 × 10−3 | 2.87635 | |
0.05 | 5.75054 × 10−5 | 5.14146 | 3.05154 × 10−4 | 4.89955 | |
0.025 | 1.12116 × 10−6 | 5.68064 | 5.26134 × 10−6 | 5.85796 |
\(h_{x}=h_{y}\) | ∥⋅∥ | Rate | \(\|\cdot \|_{\infty }\) | Rate | |
|---|---|---|---|---|---|
HOC-ADI | 0.2 | 3.10477 × 10−2 | – | 8.14136 × 10−2 | – |
0.1 | 6.97094 × 10−3 | 2.15506 | 3.07207 × 10−2 | 1.40606 | |
0.05 | 7.18499 × 10−4 | 3.27829 | 3.63248 × 10−3 | 3.08019 | |
0.025 | 4.74734 × 10−5 | 3.91979 | 2.43081 × 10−4 | 3.90144 |