Order of dissipation near rarefaction centers

Problems in the approximation of weak solutions for hyperbolic conservation-law systems by finite-difference, finite-element, or spectral projection methods are examined analytically, with a focus on the dissipation terms or mechanisms adopted to generate entropy in the presence of shocks. It is found that dissipation terms about one order of magnitude smaller than those normally used give better results in the neighborhood of rarefaction centers, although dissipation cannot be neglected in these regions. 7 references