List of Footnotes

1		Estimated from figures.
2		For W_max = 50.
3		For W_max = 50.
4		Estimated from figures.
5		Estimated from figures.
6		Estimated from figures.
7		Including points at shock transition.
8		Estimated from figures.
9		Maximum error.
10		For a Riemann problem with slightly different initial conditions.
11		For a Riemann problem with slightly different initial conditions including a nonzero transverse magnetic field.
12		All methods produce stable profiles without numerical oscillations. Comments to Martí et al. (1997) and Font et al. (1999) refer to 1D, only.
13		For a Riemann problem with slightly different initial conditions.
14		At t = 0.15.
15		For a mesh of 800 zones.
16		For a mesh of 800 zones.
17		D: excessive dissipation; O: oscillations; SE: systematic errors.
18		All finite difference methods are extended by directional splitting.
19		cAV-mono code [10 ] has improved the performance of explicit artificial-viscosity methods in dealing with ultra-relatistic flows, although the results are far from satisfactory.
20		Contains all the methods listed in Table 3 (using characteristic information) with exception of rGlimm [295 ].
21		Methods based on a exact relativistic Riemann solver can make use of the solution for non-zero transverse speeds [235 ].
22		There exist GRHD extensions of several HRSC methods based on linearized Riemann solvers. The procedure developed by Pons et al. [234 ] allows any SRHD Riemann solver to be applied to GRHD flows.
23		Important advances [143 , 14 ] although only partial success up to now.
24		Only accomplished by second-order methods [138 , 10 ].
25		Needs confirmation.
26		[150 , 262 , 204 ].
27		There is one code which considered such an extension [172 ], but the results are not completely satisfactory.