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Table 1 The convergence performance and CPU time of the coupled Algorithm 3.1 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 3.28684 0.449315 0.534235 8.793
4 0.0723105 0.273089 2.38616 0.169561 0.337904 8.793
8 0.0177107 0.107495 0.580117 0.0310711 0.154481 30.856
16 0.00418793 0.0497246 0.208445 0.00809378 0.0772969 108.743
32 0.00102092 0.0254185 0.0967607 0.00219088 0.0391418 451.241