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Theory and Modern Applications

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