Table 11 Convergence orders of \(\pmb{\mathcal {O}(h^{\mu})}\) of the decoupled Algorithm  3.4 at time \(\pmb{T=1.0}\) , with varying mesh h but fixed time step \(\pmb{\Delta t=0.01}\)

1/ h

\(\boldsymbol {\|{\mathbf{u}}_{3.4}^{m,h}-{\mathbf{u}}_{3.4}^{m,\frac{h}{2}}\|_{0}}\)

\(\boldsymbol {\rho_{{\mathbf{u}}_{f},h,0}}\)

\(\boldsymbol {\|{\mathbf{u}}_{3.4}^{m,h}-{\mathbf{u}}_{3.4}^{m,\frac{h}{2}}\|_{1}}\)

\(\boldsymbol {\rho_{{\mathbf{u}}_{f},h,1}}\)

\(\boldsymbol {\|p_{3.4}^{m,h}-p_{3.4}^{m,\frac{h}{2}}\|_{0}}\)

\(\boldsymbol {\rho_{p_{f},h,0}}\)

1/ h

\(\boldsymbol {\|\phi_{3.4}^{m,h}-\phi_{3.4}^{m,\frac{h}{2}}\|_{0}}\)

\(\boldsymbol {\rho_{\phi,h,0}}\)

\(\boldsymbol {\|\phi_{3.4}^{m,h}-\phi_{3.4}^{m,\frac{h}{2}}\|_{1}}\)

\(\boldsymbol {\rho_{\phi,h,1}}\)