Table 3.

Iteration numbers (it.), condition numbers and computational time (in s) for each preconditioning technique using ${\mathcal{P}}_2$ elements; ℓ is the level of uniform refinement. For the L2 error the definition is given in (53), while for the estimated error of convergence eoc the definition is given in (54).

all-floating
ℓ	identity prec.			lumped prec.			Dirichlet prec.			L2 error	eoc
1	149 it.	444.7	23.3 s	73 it.	73.7	22.0 s	47 it.	36.7	18.7 s	1.13E-05	-
2	129 it.	330.8	21.9 s	75 it.	74.3	20.8 s	43 it.	27.7	19.3 s	1.44E-06	2.97
3	114 it.	210.3	30.3 s	73 it.	68.8	27.3 s	36 it.	16.6	28.5 s	1.81E-07	2.99
4	105 it.	167.8	99.8 s	69 it.	65.2	93.4 s	33 it.	14.4	90.2 s	2.26E-08	3.00
classical
ℓ	identity prec.			lumped prec.			Dirichlet prec.			L2 error	eoc
1	120 it.	405.0	7.5 s	65 it.	48.9	6.9 s	40 it.	21.0	6.5 s	1.17E-05	-
2	108 it.	302.6	7.5 s	69 it.	57.6	6.7 s	41 it.	20.6	7.5 s	1.46E-06	3.00
3	112 it.	253.4	12.6 s	91 it.	116.2	11.7 s	42 it.	21.0	12.3 s	1.82E-07	3.01
4	136 it.	273.1	76.3 s	128 it.	262.8	77.3 s	48 it.	27.7	79.1 s	2.26E-08	3.01