Skip to main content

Table 9 Convergence orders of \(\pmb{\mathcal {O}(h^{\mu})}\) 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

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