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Theory and Modern Applications

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