Theory and Modern Applications
Table 1 Error and order of convergence of time discretization for example 1 ( \(\pmb{h=0.3}\) , polynomial degree \(\pmb{N=4}\) )
From: Solution of two-dimensional time-fractional Burgers equation with high and low Reynolds numbers
Δ t | α  = 0.7 | α  = 0.8 | α  = 0.9 | |||
|---|---|---|---|---|---|---|
\(\boldsymbol { \Vert e_{u} \Vert _{2}}\) | Order | \(\boldsymbol {\Vert e_{u} \Vert _{2}}\) | Order | \(\boldsymbol {\Vert e_{u} \Vert _{2}}\) | Order | |
1.0e–4 | 1.46e–04 | - | 1.46e–04 | - | 1.48e–04 | - |
5.0e–5 | 7.83e–05 | 0.90 | 7.76e–05 | 0.91 | 7.79e–05 | 0.92 |
2.5e–5 | 4.28e–05 | 0.87 | 4.23e–05 | 0.88 | 3.97e–05 | 0.97 |