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Theory and Modern Applications

Table 2 The convergence performance and CPU time of the decoupled Algorithm  3.2 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

3.29034

0.449351

0.534233

2.802

4

0.0723139

0.273084

2.38421

0.170073

0.337872

6.779

8

0.0176805

0.107496

0.580263

0.0317752

0.154487

15.092

16

0.0041693

0.0497261

0.208663

0.00894104

0.0772974

50.722

32

0.00100931

0.0254203

0.0969369

0.00323085

0.0391582

217.405