Table 3 Errors and CPU performance of the BDF2-LE scheme by using \(\pmb{(P_{2}, P_{1}, P_{2}dc)}\) finite element with \(\pmb{\triangle t=0.05h}\) and \(\pmb{T=0.1}\)
From: Convergence of a linearly extrapolated BDF2 finite element scheme for viscoelastic fluid flow
△ t | \(\boldsymbol{\vert \!\vert \!\vert e_{\sigma} \vert \!\vert \!\vert _{\infty,0}}\) | \(\boldsymbol{\vert \!\vert \!\vert e_{\sigma} \vert \!\vert \!\vert _{0,0}}\) | \(\boldsymbol{\Vert e_{\mathbf{u}} \Vert _{\infty,0}}\) | \(\boldsymbol{\vert \!\vert \!\vert \nabla e_{u}\vert \!\vert \!\vert _{0,0}}\) | \(\boldsymbol{\vert \!\vert \!\vert e_{p}\vert \!\vert \!\vert _{0,0}}\) | CPU |
|---|---|---|---|---|---|---|
1/120 | 3.09191e−3 | 8.76703e−4 | 5.05062e−4 | 6.74744e−3 | 0.0352161 | 16.61 |
1/160 | 1.47401e−3 | 3.98486e−4 | 2.06665e−4 | 3.92193e−3 | 0.0199588 | 37.535 |
1/240 | 5.53103e−4 | 1.35618e−4 | 5.93415e−5 | 1.78953e−3 | 8.87254e−3 | 125.627 |
1/320 | 2.87945e−4 | 6.56174e−5 | 2.58288e−5 | 1.01788e−3 | 4.94498e−3 | 317.612 |
1/480 | 1.19708e−4 | 2.50901e−5 | 1.11776e−5 | 4.57881e−4 | 2.12907e−3 | 1,124.82 |
order | 2.35658 | 2.57344 | 2.78518 | 1.93818 | 2.02091 |