Table 7.

Tracy problem scaling parameter $d_{K,m}$ given by (21b), approximation of the error and the error estimators, EOC in parenthesis

h	$\#\text{DoF}$	$\tilde{\mathcal{R}}(u_h^{\tau })$	$\eta$	$\mathcal{J}(u_h^{\tau })$	${\eta }_R$	${\eta }_S$	${\eta }_T$	$i_{\text{eff}}$	$i_{\text{eff}}^{\text{tot}}$
$\text{p}=1$ & $\text{q}=1$
0.18	384	$2.43\times {10}^{-1}$	$2.95\times {10}^{-1}$	$6.62\times 102$	$2.25\times {10}^{-3}$	$2.90\times {10}^{-1}$	$4.83\times {10}^{-2}$	1.22	1.00
0.09	1536	$8.77\times {10}^{-2}$	$1.19\times {10}^{-1}$	$2.47\times 102$	$9.92\times {10}^{-4}$	$1.10\times {10}^{-1}$	$4.36\times {10}^{-2}$	1.35	1.00
		(1.47 )	(1.32)	(1.43)	(1.18)	(1.40)	(0.15)
0.04	6144	$1.50\times {10}^{-2}$	$2.51\times {10}^{-2}$	$4.68\times 101$	$1.33\times {10}^{-4}$	$2.39\times {10}^{-2}$	$7.31\times {10}^{-3}$	1.67	1.00
		(2.55)	(2.24)	(2.40)	(2.90)	(2.20)	(2.58)
0.02	24576	$7.34\times {10}^{-3}$	$1.22\times {10}^{-2}$	$2.27\times 101$	$8.11\times {10}^{-5}$	$1.20\times {10}^{-2}$	$1.86\times {10}^{-3}$	1.66	1.00
		(1.03)	(1.04)	(1.05)	(0.71)	(0.99)	(1.98)
$\text{p}=2$ & $\text{q}=2$
0.18	768	$4.88\times {10}^{-2}$	$6.18\times {10}^{-2}$	$1.92\times 102$	$3.35\times {10}^{-4}$	$6.04\times {10}^{-2}$	$1.22\times {10}^{-2}$	1.27	1.00
0.09	3072	$1.75\times {10}^{-2}$	$1.98\times {10}^{-2}$	$6.03\times 101$	$1.44\times {10}^{-5}$	$1.95\times {10}^{-2}$	$3.35\times {10}^{-3}$	1.13	1.00
		(1.48)	(1.65)	(1.67)	(4.54)	(1.63)	(1.86)
0.04	12288	$5.59\times {10}^{-3}$	$6.28\times {10}^{-3}$	$1.94\times 101$	$4.68\times {10}^{-6}$	$6.08\times {10}^{-3}$	$1.56\times {10}^{-3}$	1.12	1.00
		(1.64)	(1.65)	(1.64)	(1.62)	(1.68)	(1.11)
0.02	49,152	$1.90\times {10}^{-3}$	$1.33\times {10}^{-3}$	4.37	$2.41\times {10}^{-6}$	$1.31\times {10}^{-3}$	$1.87\times {10}^{-4}$	0.70	1.00
		(1.56)	(2.24)	(2.15)	(0.96)	(2.21)	(3.06)
$\text{p}=3$ & $\text{q}=2$
0.18	1280	$2.24\times {10}^{-2}$	$2.64\times {10}^{-2}$	$9.60\times 101$	$2.42\times {10}^{-5}$	$2.61\times {10}^{-2}$	$4.48\times {10}^{-3}$	1.18	1.00
0.09	5120	$6.26\times {10}^{-3}$	$7.94\times {10}^{-3}$	$2.77\times 101$	$1.21\times {10}^{-5}$	$7.13\times {10}^{-3}$	$3.48\times {10}^{-3}$	1.27	1.00
		(1.84)	(1.74)	(1.79)	(1.00)	(1.87)	(0.37)
0.04	20480	$1.40\times {10}^{-3}$	$4.60\times {10}^{-4}$	1.63	$2.87\times {10}^{-6}$	$4.49\times {10}^{-4}$	$8.90\times {10}^{-5}$	0.33	1.00
		(2.16)	(4.11)	(4.08)	(2.08)	(3.99)	(5.29)
0.02	81920	$1.37\times {10}^{-3}$	$8.85\times {10}^{-5}$	$3.08\times {10}^{-1}$	$2.37\times {10}^{-6}$	$8.59\times {10}^{-5}$	$1.09\times {10}^{-5}$	0.06	1.00
		(0.03)	(2.38)	(2.41)	(0.28)	(2.39)	(3.03)