Table 2.

Mesh details for flow and Lagrange multiplier domains, Ω_f and Ω_λ

		Refinement	Number of elements		Number of nodes		Avrg. runtime
Phase	Scheme	level	$N_f^e$ // $N_{\lambda }^e$	v f	φ f	λ	per time step	Number of cores
I	inf‐sup st.	rl‐1	127 774  //    3424	195 635	27 914	6875	13.89 s	16
	inf‐sup st.	rl‐2	158 236  //    3424	236 137	32 934	6875	22.10 s	16
	inf‐sup st.	rl‐3	333 048  //    3424	469 487	62 203	6875	38.72 s	16
	cG(1)cG(1)	rl‐ $\tilde{1}$	673 066  //  54 784	133 663	133 663	27 445	21.01 s	16
	inf‐sup st.	rl‐1‐trunc	135 352  //    3424	207 431	29 615	6875	10.39 s	16
	inf‐sup st.	rl‐2‐trunc	152 126  //    3424	229 725	32 375	6875	13.04 s	16
II	inf‐sup st.	rl‐1	131 263  //    3424	200 276	28 490	6875	12.60 s	16
	inf‐sup st.	rl‐2	166 205  //    3424	246 812	34 287	6875	14.86 s	16
	inf‐sup st.	rl‐3	351 221  //    3424	493 664	65 205	6875	38.72 s	16
	cG(1)cG(1)	rl‐ $\tilde{1}$	673 066  //  54 784	133 663	133 663	27 445	50.53 s	32
	inf‐sup st.	rl‐1‐trunc	136 955  //    3424	209 562	29 879	6875	13.16 s	16
	inf‐sup st.	rl‐2‐trunc	160 539  //    3424	241 002	33 807	6875	14.61 s	16

The solid domain was discretized using 1430 elements with 15 065 nodes for u _s and 2376 nodes for φ _s.