Theory and Modern Applications
From: Stability and convergence of some novel decoupled schemes for the non-stationary Stokes-Darcy model
1/ h | \(\boldsymbol {\|{\mathbf{u}}_{3.2}^{m,h}-{\mathbf{u}}_{3.2}^{m,\frac{h}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{{\mathbf{u}}_{f},h,0}}\) | \(\boldsymbol {\|{\mathbf{u}}_{3.2}^{m,h}-{\mathbf{u}}_{3.2}^{m,\frac{h}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{{\mathbf{u}}_{f},h,1}}\) | \(\boldsymbol {\|p_{3.2}^{m,h}-p_{3.2}^{m,\frac{h}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{p_{f},h,0}}\) |
---|---|---|---|---|---|---|
2 | 0.2151001 | 3.80355 | 1.65021 | 1.91075 | 0.940921 | 1.50545 |
4 | 0.0565524 | 3.86866 | 0.863644 | 1.93151 | 0.625008 | 2.43456 |
8 | 0.0146181 | 4.0458 | 0.447135 | 2.13698 | 0.256723 | 2.85632 |
16 | 0.00361315 | 0.209237 | 0.089879 |
1/ h | \(\boldsymbol {\|\phi_{3.2}^{m,h}-\phi_{3.2}^{m,\frac{h}{2}}\|_{0}}\) | \(\boldsymbol {\rho_{\phi,h,0}}\) | \(\boldsymbol {\|\phi_{3.2}^{m,h}-\phi_{3.2}^{m,\frac{h}{2}}\|_{1}}\) | \(\boldsymbol {\rho_{\phi,h,1}}\) |
---|---|---|---|---|
2 | 0.135254 | 3.31099 | 1.30796 | 1.68767 |
4 | 0.04085 | 4.07816 | 0.775011 | 1.90658 |
8 | 0.0100168 | 4.18833 | 0.406494 | 1.98302 |
16 | 0.00239159 | 0.204987 |