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Table 4: Advection of cosine hill in rotation.

CN-LSFEM ST-LSFEM BE-LSFEM Improvements Range of PCG iterations* Δt Courant no.‡ $U_{\min \hspace{0.17em}}$ $U_{\max \hspace{0.17em}}$ $U_{\min \hspace{0.17em}}$ $U_{\max \hspace{0.17em}}$ $U_{\min \hspace{0.17em}}$ $U_{\max \hspace{0.17em}}$ %redn. in $U_{\min \hspace{0.17em}}$ %gain in $U_{\max \hspace{0.17em}}$ 2π/120 0.2618 $-$0.0265 0.9691 $-$0.0405 0.958 $-$0.0189 0.9769 28.8 0.81 7-8 2π/60 0.5236 $-$0.0615 0.9165 $-$0.1138 0.8872 $-$0.0270 0.9713 56.1 5.98 8-8 2π/30 1.047 $-$0.2009 0.8369 $-$0.2192 0.7398 $-$0.2129 0.8418 $-$5.97 0.6 15-16

‡Courant number based on velocity of the peak.*Range of PCG iterations/time step: number of iterations with one bubble—the number with six bubbles. % Reduction and % gain calculated on Crank-Nicolson LSFEM results as baseline.