Table 4
Approximation of (42) with a nonlinear DDFV scheme [62, 63] on the Kershaw mesh family from [93], final time T = 0.25. M is the mesh index, τ is the time step, errgs and errs respectively stand for the L 2(Ω × (0, T)) error on ∇ s and the L ∞((0, T); L 2(Ø)) error on s, whereas ordgs and ords are the corresponding convergence orders. N max and N mean are the maximal and mean numbers of Newton iterations, and s min minimal value of the approximation of s during the whole simulation.
| M | τ | errgs | ordgs | errs | ords | N max | N mean | s min |
|---|---|---|---|---|---|---|---|---|
| 1 | 2.0E-03 | 6.693E-02 | – | 7.254E-03 | – | 9 | 2.15 | 1.010E-01 |
| 2 | 5.0E-04 | 2.353E-02 | 1.54 | 1.751E-03 | 2.09 | 8 | 2.02 | 2.582E-02 |
| 3 | 1.25E-04 | 1.235E-02 | 1.61 | 7.237E-04 | 2.20 | 7 | 1.49 | 6.488E-03 |
| 4 | 3.125E-05 | 7.819E-03 | 1.60 | 3.962E-04 | 2.11 | 7 | 1.07 | 1.628E-03 |
| 5 | 3.125E-05 | 5.507E-03 | 1.58 | 2.556E-04 | 1.98 | 7 | 1.04 | 1.628E-03 |