Table 6.
Accuracy and convergence of the Prony approximation with Δt and N applied to the ideal analytic solution. Percentage errors were measured relative to the GL with a refined time-step size of Δt = 1e-5. The percentage errors reported in the table correspond to the L 2(0, T) norm difference in (1,3)-Cauchy stress component normalized by the L 2(0, T) norm of the (1,3)-Cauchy stress component predicted by the reference solution.
| Δt (s) | Prony error (%) | |||
|---|---|---|---|---|
| N = 3 | N = 6 | N = 9 | N = 12 | |
| 1e–2 | 2.26e0 | 5.05e–1 | 6.51e–1 | 7.01e–1 |
| 5e–3 | 2.06e0 | 1.52e–1 | 2.50e–1 | 3.27e–1 |
| 1e–3 | 2.00e0 | 1.01e–1 | 1.30e–2 | 1.97e–2 |
| 5e–4 | 1.99e0 | 1.04e–1 | 8.79e–3 | 4.86e–3 |