@Article{bouchut09semi-discrete,
  author   = {Bouchut, Fran{\c{c}}ois and Morales de Luna, Tom{\'a}s},
  title    = {{S}emi-discrete {E}ntropy {S}atisfying {A}pproximate {R}iemann {S}olvers. {T}he {C}ase of the {S}uliciu {R}elaxation {A}pproximation},
  journal  = {Journal of Scientific Computing},
  year     = {2009},
  volume   = {41},
  number   = {3},
  pages    = {483-509},
  abstract = {Abstract In this work we establish conditions for an approximate simple
	Riemann solver to satisfy a semi-discrete entropy inequality. The
	semi-discrete approach is less restrictive than the fully-discrete
	case and allows to grant some other good properties for numerical
	schemes. First, conditions are established in an abstract framework
	for simple Riemann solvers to satisfy a semi-discrete entropy inequality
	and then the results are applied, as a particular case, to the Suliciu
	system. This will lead in particular to the definition of schemes
	for the isentropic gas dynamics and the full gas dynamics system
	that are stable and preserve the stationary shocks.},
  url      = {http://dx.doi.org/10.1007/s10915-009-9311-3},
}

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