Table 4.

Barenblatt problem (96)–(97), $m=2$, scaling parameter $d_{K,m}$ given by (21b), approximation of the error and the error estimators, EOC in parenthesis

h	$\#\text{DoF}$	$\tilde{\mathcal{R}}(u_h^{\tau })$	$\eta$	$\mathcal{J}(u_h^{\tau })$	${\eta }_R$	${\eta }_S$	${\eta }_T$	$i_{\text{eff}}$	$i_{\text{eff}}^{\text{tot}}$
$\text{p}=1$ & $\text{q}=1$
1.41	864	$3.35\times {10}^{-1}$	$5.76\times {10}^{-1}$	1.59	$6.44\times {10}^{-5}$	$4.58\times {10}^{-1}$	$3.50\times {10}^{-1}$	1.72	1.13
0.71	3456	$8.54\times {10}^{-2}$	$1.60\times {10}^{-1}$	$3.84\times {10}^{-1}$	$2.95\times {10}^{-5}$	$1.37\times {10}^{-1}$	$8.19\times {10}^{-2}$	1.87	1.16
		(1.97)	(1.85)	(2.05)	(1.13)	(1.74)	(2.09)
0.35	13824	$2.74\times {10}^{-2}$	$5.68\times {10}^{-2}$	$1.14\times {10}^{-1}$	$1.20\times {10}^{-5}$	$5.43\times {10}^{-2}$	$1.68\times {10}^{-2}$	2.07	1.21
		(1.64)	(1.49)	(1.75)	(1.29)	(1.34)	(2.29)
0.18	55296	$1.15\times {10}^{-2}$	$2.57\times {10}^{-2}$	$4.53\times {10}^{-2}$	$4.56\times {10}^{-6}$	$2.55\times {10}^{-2}$	$3.03\times {10}^{-3}$	2.22	1.25
		(1.25)	(1.15)	(1.34)	(1.40)	(1.09)	(2.47)
0.09	221184	$5.54\times {10}^{-3}$	$1.27\times {10}^{-2}$	$2.13\times {10}^{-2}$	$1.64\times {10}^{-6}$	$1.26\times {10}^{-2}$	$6.05\times {10}^{-4}$	2.29	1.27
		(1.06)	(1.02)	(1.09)	(1.48)	(1.01)	(2.32)
$\text{p}=2$ & $\text{q}=2$
1.41	1728	$6.33\times {10}^{-2}$	$1.27\times {10}^{-1}$	$4.52\times {10}^{-1}$	$1.98\times {10}^{-5}$	$9.68\times {10}^{-2}$	$8.18\times {10}^{-2}$	2.00	1.12
0.71	6912	$1.63\times {10}^{-2}$	$2.99\times {10}^{-2}$	$1.10\times {10}^{-1}$	$8.16\times {10}^{-6}$	$2.35\times {10}^{-2}$	$1.85\times {10}^{-2}$	1.84	1.11
		(1.96)	(2.08)	(2.04)	(1.28)	(2.04)	(2.14)
0.35	27648	$4.78\times {10}^{-3}$	$7.49\times {10}^{-3}$	$2.94\times {10}^{-2}$	$3.10\times {10}^{-6}$	$6.52\times {10}^{-3}$	$3.69\times {10}^{-3}$	1.57	1.08
		(1.77)	(2.00)	(1.90)	(1.40)	(1.85)	(2.33)
0.18	110592	$1.55\times {10}^{-3}$	$2.15\times {10}^{-3}$	$9.04\times {10}^{-3}$	$1.13\times {10}^{-6}$	$2.04\times {10}^{-3}$	$6.62\times {10}^{-4}$	1.39	1.06
		(1.63)	(1.80)	(1.70)	(1.46)	(1.67)	(2.48)
$\text{p}=3$ & $\text{q}=2$
1.41	2880	$2.57\times {10}^{-2}$	$5.65\times {10}^{-2}$	$2.00\times {10}^{-1}$	$1.26\times {10}^{-5}$	$3.69\times {10}^{-2}$	$4.28\times {10}^{-2}$	2.20	1.14
0.71	11520	$7.54\times {10}^{-3}$	$1.35\times {10}^{-2}$	$5.31\times {10}^{-2}$	$4.33\times {10}^{-6}$	$1.03\times {10}^{-2}$	$8.70\times {10}^{-3}$	1.79	1.10
		(1.77)	(2.06)	(1.91)	(1.54)	(1.84)	(2.30)
0.35	46080	$2.51\times {10}^{-3}$	$3.76\times {10}^{-3}$	$1.68\times {10}^{-2}$	$1.53\times {10}^{-6}$	$3.34\times {10}^{-3}$	$1.73\times {10}^{-3}$	1.50	1.06
		(1.59)	(1.85)	(1.66)	(1.50)	(1.63)	(2.33)
0.18	184320	$8.71\times {10}^{-4}$	$1.18\times {10}^{-3}$	$5.64\times {10}^{-3}$	$5.42\times {10}^{-7}$	$1.14\times {10}^{-3}$	$3.09\times {10}^{-4}$	1.36	1.05
		(1.53)	(1.67)	(1.57)	(1.50)	(1.55)	(2.48)