Theory and Modern Applications
From: Stability and convergence of some novel decoupled schemes for the non-stationary Stokes-Darcy model
1/ h | \(\boldsymbol {\|{\mathbf{u}}_{3.4}^{m,h}-{\mathbf{u}}_{3.4}^{m,\frac{h}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{{\mathbf{u}}_{f},h,0}}\) | \(\boldsymbol {\|{\mathbf{u}}_{3.4}^{m,h}-{\mathbf{u}}_{3.4}^{m,\frac{h}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{{\mathbf{u}}_{f},h,1}}\) | \(\boldsymbol {\|p_{3.4}^{m,h}-p_{3.4}^{m,\frac{h}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{p_{f},h,0}}\) |
---|---|---|---|---|---|---|
2 | 0.215106 | 3.80487 | 1.65033 | 1.91101 | 0.941814 | 1.50623 |
4 | 0.0565345 | 3.86891 | 0.86359 | 1.93145 | 0.625278 | 2.43518 |
8 | 0.0146125 | 4.04563 | 0.447119 | 2.13703 | 0.256769 | 2.85676 |
16 | 0.00361192 | 0.209225 | 0.0898811 |
1/ h | \(\boldsymbol {\|\phi_{3.4}^{m,h}-\phi_{3.4}^{m,\frac{h}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{\phi,h,0}}\) | \(\boldsymbol {\|\phi_{3.4}^{m,h}-\phi_{3.4}^{m,\frac{h}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{\phi,h,1}}\) |
---|---|---|---|---|
2 | 0.135175 | 3.3141 | 1.30791 | 1.68817 |
4 | 0.0407879 | 4.07829 | 0.774753 | 1.90637 |
8 | 0.0100012 | 4.18768 | 0.406401 | 1.98302 |
16 | 0.00238826 | 0.204943 |