@article{morales_de_luna_relation_2014,
	title = {Relation between {PVM} schemes and simple Riemann solvers},
	volume = {30(4)},
	url = {http://onlinelibrary.wiley.com/doi/10.1002/num.21871/abstract},
	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},
	pages = {1315--1341},
	journaltitle = {Numerical Methods for Partial Differential Equations},
	author = {Morales de Luna, Tomás and Castro Díaz, Manuel J. and Parés, Carlos},
	date = {2014-03},
	keywords = {finite volume schemes, {PVM} schemes, Riemann solvers, Shallow water equations},
}

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