@Article{MoralesdeLuna2014,
  author   = {Morales de Luna, Tom{\'a}s and Castro D{\'i}az, Manuel J. and Par{\'e}s, Carlos},
  journal  = {Numerical Methods for Partial Differential Equations},
  title    = {{R}elation between {PVM} schemes and simple {R}iemann solvers},
  year     = {2014},
  month    = {mar},
  pages    = {1315-1341},
  volume   = {30(4)},
  abstract = {Approximate Riemann solvers (ARS) and polynomial viscosity matrix
	(PVM) methods constitute two general frameworks to derive numerical
	schemes for hyperbolic systems of Partial Differential Equations
	(PDE's). In this work, the relation between these two frameworks
	is analyzed: we show that every PVM method can be interpreted in
	terms of an approximate Riemann solver provided that it is based
	on a polynomial that interpolates the absolute value function at
	some points. Furthermore, the converse is true provided that the
	ARS satisfies a technical property to be specified. Besides its
	theoretical interest, this relation provides a useful tool to investigate
	the properties of some well-known numerical methods that are particular
	cases of PVM methods, as the analysis of some properties is easier
	for ARS methods. We illustrate this usefulness by analyzing the
	positivity-preservation property of some well-known numerical methods
	for the shallow water system. © 2014 Wiley Periodicals, Inc. Numer
	Methods Partial Differential Eq, 2014},
  keywords = {finite volume schemes, PVM schemes, Riemann solvers, Shallow water equations},
  url      = {http://onlinelibrary.wiley.com/doi/10.1002/num.21871/abstract},
}

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