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Table 3
L1-norm of the error for the vortex advection problem for a resolution of 2562.
| Method | ϵ = 10-2 | ϵ = 10-4 | ϵ = 10-6 |
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| Exact Newton | 5.2710(–6) | 5.3230(–7) | 5.2788(–7) |
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| Inexact Newton (η = 10-6) | 5.2704(–6) | 5.3226(–7) | 5.2788(–7) |
| w/o preconditioner | 5.2710(–6) | 5.3233(–7) | 5.2788(–7) |
| Inexact Broyden (η = 10-6) | 5.2704(–6) | 5.6946(–7) | 5.2788(–7) |
| w/o preconditioner | 5.2710(–6) | 5.6970(–7) | 5.2788(–7) |
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| Inexact Newton (η = 10-4) | 5.2434(–6) | 5.3212(–7) | 5.2788(–7) |
| w/o preconditioner | 5.4118(–6) | 5.3293(–7) | 5.2788(–7) |
| Inexact Broyden (η = 10-4) | 5.2434(–6) | 5.6980(–7) | 5.2786(–7) |
| w/o preconditioner | 1.1380(–5) | 5.7081(–7) | 5.2788(–7) |
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| Inexact Newton (η = 10-2) | 6.6104(–6) | 5.3091(–7) | 5.2789(–7) |
| w/o preconditioner | 1.1381(–5) | 6.3107(–7) | 5.2788(–7) |
| Inexact Broyden (η = 10-2) | 6.6104(–6) | 5.6907(–7) | 5.2790(–7) |
| w/o preconditioner | 1.1380(–5) | 5.4528(–7) | 5.2799(–7) |
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| Inexact Newton (η = 10-1) | 3.6799(–5) | 1.3171(–6) | 5.2787(–7) |
| w/o preconditioner | 8.1637(–5) | 9.4765(–7) | 5.2794(–7) |
| Inexact Broyden (η = 10-1) | 3.6799(–5) | 2.3078(–6) | 5.2799(–7) |
| w/o preconditioner | 8.1641(–5) | 1.1158(–6) | 5.2793(–7) |
Notes. ϵ is the nonlinear tolerance of the Newton-Raphson procedure, and η the linear tolerance of the Krylov solver.
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