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Theory and Modern Applications

Table 6 The convergence performance and CPU time of the decoupled Algorithm  3.2 at time \(\pmb{T=1.0}\) , with varying time step Δ t but fixed mesh \(\pmb{h=\frac{1}{32}}\)

From: Stability and convergence of some novel decoupled schemes for the non-stationary Stokes-Darcy model

Δ t

\(\boldsymbol {\frac{\|{\mathbf{u}}_{f}-{\mathbf{u}}^{m,h}_{3.4}\|_{0}}{\|{\mathbf{u}}_{f}\|_{0}}}\)

\(\boldsymbol {\frac{\|{\mathbf{u}}_{f}-{\mathbf{u}}^{m,h}_{3.4}\|_{1}}{\|{\mathbf{u}}_{f}\|_{1}}}\)

\(\boldsymbol {\frac{\|p_{f}-p^{m,h}_{3.4}\|_{0}}{\|p_{f}\|_{0}}}\)

\(\boldsymbol {\frac{\|\phi-\phi^{m,h}_{3.4}\|_{0}}{\|\phi\|_{0}}}\)

\(\boldsymbol {\frac{\|\phi-\phi^{m,h}_{3.4}\|_{1}}{\|\phi\|_{1}}}\)

CPU(S)

0.1

0.00157101

0.0256652

0.110761

0.0160073

0.0407084

20.607

0.05

0.00109152

0.0254802

0.100058

0.00890671

0.0395539

42.095

0.025

0.000949681

0.0254322

0.0977095

0.00534402

0.0392473

88.186

0.0125

0.000992267

0.0254214

0.0969716

0.00355753

0.0391676

184.475