Table 2 Numerical results of the Euler implicit/explicit scheme at time \(\pmb{T=1.0}\) with varying time step Δ t but fixed mesh size \(\pmb{h=\frac{1}{32}}\)

Δ t

\(\boldsymbol {\frac{\|u-u^{n}\|_{0}}{\|u\|_{0}}}\)

\(\boldsymbol {\frac{\|\nabla(u-u^{n})\|_{0}}{\|\nabla u\|_{0}}}\)

\(\boldsymbol {\frac{\|p-p^{n}\|_{0}}{\|p\|_{0}}}\)

\(\boldsymbol {\frac{\|\theta-\theta^{n}\|_{0}}{\|\theta\|_{0}}}\)

\(\boldsymbol {\frac{\|\nabla(\theta-\theta^{n})\|_{0}}{\|\nabla\theta\|_{0}}}\)

CPU(S)