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Table 10 Convergence orders of \(\pmb{\mathcal {O}(h^{\mu})}\) 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

1/ h \(\boldsymbol {\|{\mathbf{u}}_{3.3}^{m,h}-{\mathbf{u}}_{3.3}^{m,\frac{h}{2}}\|_{0}}\) \(\boldsymbol {\rho_{{\mathbf{u}}_{f},h,0}}\) \(\boldsymbol {\|{\mathbf{u}}_{3.3}^{m,h}-{\mathbf{u}}_{3.3}^{m,\frac{h}{2}}\|_{1}}\) \(\boldsymbol {\rho_{{\mathbf{u}}_{f},h,1}}\) \(\boldsymbol {\|p_{3.3}^{m,h}-p_{3.3}^{m,\frac{h}{2}}\|_{0}}\) \(\boldsymbol {\rho_{p_{f},h,0}}\)
2 0.215099 3.80338 1.6502 1.91072 0.940517 1.50494
4 0.0565547 3.86854 0.863652 1.93151 0.624954 2.43437
8 0.0146192 4.04581 0.447138 2.13698 0.256721 2.85629
16 0.00361342   0.209238   0.0898792  
1/ h \(\boldsymbol {\|\phi_{3.3}^{m,h}-\phi_{3.3}^{m,\frac{h}{2}}\|_{0}}\) \(\boldsymbol {\rho_{\phi,h,0}}\) \(\boldsymbol {\|\phi_{3.3}^{m,h}-\phi_{3.3}^{m,\frac{h}{2}}\|_{1}}\) \(\boldsymbol {\rho_{\phi,h,1}}\)
2 0.135335 3.3074 1.30801 1.68713
4 0.0409188 4.07757 0.775285 1.90679
8 0.0100351 4.18889 0.406592 1.98307
16 0.00239564   0.205032