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A Genuinely High Order Total Variation Diminishing Scheme for One-Dimensional Scalar Conservation Laws
2010
SIAM Journal on Numerical Analysis
It is well known that finite difference or finite volume total variation diminishing (TVD) schemes solving one-dimensional scalar conservation laws degenerate to first order accuracy at smooth extrema [S. Osher and S. Chakravarthy, SIAM J. Numer. Anal., 21 (1984), pp. 955-984], thus TVD schemes are at most second order accurate in the L 1 norm for general smooth and nonmonotone solutions. However, Sanders [Math. Comp., 51 (1988), pp. 535-558] introduced a third order accurate finite volume
doi:10.1137/090764384
fatcat:klsgvzoamfce5d3m37uykn4euu