Theory and Modern Applications
Table 2 The convergence rate for \(\pmb{\|\mathbf {z}-\mathbf {z}_{h}\|_{\mathbf {L}^{2}_{\varepsilon}}}\) in the two-dimensional case
h = Δ t | \(\boldsymbol{\|\mathbf {z}-\mathbf {z}_{h}\|_{\mathbf {L}^{2}_{\varepsilon}}}\) | |||
|---|---|---|---|---|
ε = 0.001 | ε = 0.0005 | ε = 0.0001 | ε = 0.00005 | |
1/16 | 4.8981e−04 | 5.0423e−04 | 5.1575e−04 | 5.1719e−04 |
1/32 | 3.1965e−04 | 3.3192e−04 | 3.4191e−04 | 3.4317e−04 |
1/48 | 1.5467e−04 | 1.6197e−04 | 1.6828e−04 | 1.6911e−04 |
1/64 | 1.1503e−04 | 1.2055e−04 | 1.2548e−04 | 1.2614e−04 |
Convergence rate 1.0526 | Constant \(\bar{Q}_{2}=0.0041\) | |||