Table 4: L₁ norm errors of the density and convergence rate (r) under grid refinement for problem 4 at t=0.4. Results for three schemes (Marquina, HLLE, and Tadmor) and two reconstruction procedures (PPM and PHM) are shown.

Scheme	N	L1 (10-2)		r
		PPM	PHM	PPM	PHM
Marquina	50	14.8	23.2	-	-
	100	21.0	18.5	-0.50	0.30
	200	16.1	15.1	0.38	0.32
	400	8.99	11.4	0.84	0.41
	800	4.22	7.22	1.09	0.66
	1600	2.22	3.87	0.93	0.90
	3200	1.04	2.06	1.09	0.91
HLLE	50	14.8	23.3	-	-
	100	20.9	17.0	-0.50	0.29
	200	16.1	15.1	0.38	0.33
	400	8.99	11.4	0.84	0.41
	800	4.22	7.22	1.09	0.66
	1600	2.22	3.87	0.93	0.90
	3200	1.04	2.06	1.09	0.91
Tadmor	50	14.7	23.6	-	-
	100	20.7	19.1	-0.49	0.30
	200	16.0	15.2	0.37	0.33
	400	8.94	11.0	0.84	0.47
	800	4.19	7.26	1.09	0.60
	1600	2.21	3.89	0.92	0.90
	3200	1.04	2.07	1.09	0.91