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Table 6 The convergence performance and CPU time of the decoupled Algorithm  3.2 at time \(\pmb{T=1.0}\) , with varying time step Δ t but fixed mesh \(\pmb{h=\frac{1}{32}}\)

From: Stability and convergence of some novel decoupled schemes for the non-stationary Stokes-Darcy model

Δ t \(\boldsymbol {\frac{\|{\mathbf{u}}_{f}-{\mathbf{u}}^{m,h}_{3.4}\|_{0}}{\|{\mathbf{u}}_{f}\|_{0}}}\) \(\boldsymbol {\frac{\|{\mathbf{u}}_{f}-{\mathbf{u}}^{m,h}_{3.4}\|_{1}}{\|{\mathbf{u}}_{f}\|_{1}}}\) \(\boldsymbol {\frac{\|p_{f}-p^{m,h}_{3.4}\|_{0}}{\|p_{f}\|_{0}}}\) \(\boldsymbol {\frac{\|\phi-\phi^{m,h}_{3.4}\|_{0}}{\|\phi\|_{0}}}\) \(\boldsymbol {\frac{\|\phi-\phi^{m,h}_{3.4}\|_{1}}{\|\phi\|_{1}}}\) CPU(S)
0.1 0.00157101 0.0256652 0.110761 0.0160073 0.0407084 20.607
0.05 0.00109152 0.0254802 0.100058 0.00890671 0.0395539 42.095
0.025 0.000949681 0.0254322 0.0977095 0.00534402 0.0392473 88.186
0.0125 0.000992267 0.0254214 0.0969716 0.00355753 0.0391676 184.475