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Table 4 The convergence performance and CPU time of the decoupled Algorithm  3.4 at time \(\pmb{T=1.0}\) , with varying mesh h but fixed time step \(\pmb{\Delta t=0.01}\)

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

\(\boldsymbol {\frac{1}{h}}\) \(\boldsymbol {\frac{\|{\mathbf{u}}_{f}-{\mathbf{u}}^{m,h}_{3.4}\|_{0}}{\|{\mathbf{u}}_{f}\|_{0}}}\) \(\boldsymbol {\frac{\|{\mathbf{u}}_{f}-{\mathbf{u}}^{m,h}_{3.4}\|_{1}}{\|{\mathbf{u}}_{f}\|_{1}}}\) \(\boldsymbol {\frac{\|p_{f}-p^{m,h}_{3.4}\|_{0}}{\|p_{f}\|_{0}}}\) \(\boldsymbol {\frac{\|\phi-\phi^{m,h}_{3.4}\|_{0}}{\|\phi\|_{0}}}\) \(\boldsymbol {\frac{\|\phi-\phi^{m,h}_{3.4}\|_{1}}{\|\phi\|_{1}}}\) CPU(S)
2 0.256573 0.402367 3.28676 0.449351 0.534233 2.867
4 0.0723103 0.273089 2.3867 0.170064 0.337873 6.766
8 0.0177147 0.107495 0.580137 0.0317483 0.154487 13.298
16 0.00419167 0.0497249 0.208433 0.00890173 0.0772969 49.513
32 0.0010238 0.0254187 0.0968278 0.00317698 0.0391566 224.978