Numerical methods and HPC
Open Access

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

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.