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Table 3 The convergence performance and CPU time of the decoupled Algorithm  3.3 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 3.29042 0.449315 0.534235 2.814
4 0.0723142 0.273084 2.38369 0.169569 0.337904 6.782
8 0.0176767 0.107497 0.580288 0.0310971 0.154481 13.987
16 0.00416661 0.0497265 0.208831 0.00812777 0.0772966 46.337
32 0.00100802 0.0254209 0.097102 0.00223235 0.039142 219.175