Theory and Modern Applications
From: Stability and convergence of some novel decoupled schemes for the non-stationary Stokes-Darcy model
1/ h | \(\boldsymbol {\|{\mathbf{u}}_{3.3}^{m,h}-{\mathbf{u}}_{3.3}^{m,\frac{h}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{{\mathbf{u}}_{f},h,0}}\) | \(\boldsymbol {\|{\mathbf{u}}_{3.3}^{m,h}-{\mathbf{u}}_{3.3}^{m,\frac{h}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{{\mathbf{u}}_{f},h,1}}\) | \(\boldsymbol {\|p_{3.3}^{m,h}-p_{3.3}^{m,\frac{h}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{p_{f},h,0}}\) |
---|---|---|---|---|---|---|
2 | 0.215099 | 3.80338 | 1.6502 | 1.91072 | 0.940517 | 1.50494 |
4 | 0.0565547 | 3.86854 | 0.863652 | 1.93151 | 0.624954 | 2.43437 |
8 | 0.0146192 | 4.04581 | 0.447138 | 2.13698 | 0.256721 | 2.85629 |
16 | 0.00361342 | 0.209238 | 0.0898792 |
1/ h | \(\boldsymbol {\|\phi_{3.3}^{m,h}-\phi_{3.3}^{m,\frac{h}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{\phi,h,0}}\) | \(\boldsymbol {\|\phi_{3.3}^{m,h}-\phi_{3.3}^{m,\frac{h}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{\phi,h,1}}\) |
---|---|---|---|---|
2 | 0.135335 | 3.3074 | 1.30801 | 1.68713 |
4 | 0.0409188 | 4.07757 | 0.775285 | 1.90679 |
8 | 0.0100351 | 4.18889 | 0.406592 | 1.98307 |
16 | 0.00239564 | 0.205032 |