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Table 3 Numerical results of the standard Galerkin FEM at time \(\pmb{T=1.0}\) with varying mesh size h but fixed time step \(\pmb{\Delta t=0.01}\)

From: The Euler implicit/explicit scheme for the Boussinesq equations

\(\boldsymbol {\frac{1}{h}}\)

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

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

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

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

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

CPU(S)

4

0.0225932

0.24839

0.698555

0.0209496

0.15429

14.898

9

0.0085461

0.116535

0.152122

0.00558951

0.078966

23.744

16

0.00247039

0.054131

0.0461534

0.00147279

0.0410255

46.129

25

0.000621059

0.0259783

0.0136212

0.000377335

0.0207576

208.163

36

0.000155184

0.0127744

0.00416879

0.000101501

0.0104133

1,063.48