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Theory and Modern Applications

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