Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions

  title={Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions},
  author={Philippe G. LeFloch and Jian-Guo Liu},
  journal={Math. Comput.},
Solutions of conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this property from a numerical standpoint. We introduce a class of fully discrete in space and time, high order accurate, difference schemes, called generalized monotone schemes. Convergence toward the entropy solution is proven via a new technique of proof, assuming… CONTINUE READING

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The one-sided Lipschitz condition for convex scalar conservation laws

  • Y. Brenier, S. J. Osher
  • SIAM J. Numer. Anal
  • 1988
Highly Influential
8 Excerpts

Towards the ultimate conservative difference scheme, II, Monotonicity and conservation combined in a second order scheme

  • B. van Leer
  • J. Comp. Phys
  • 1974
Highly Influential
7 Excerpts

On the convergence of difference approximations to scalar conservation

  • S. J. Osher, E. Tadmor
  • laws, Math. of Comp
  • 1988
Highly Influential
8 Excerpts

Decay of solutions of nonlinear hyperbolic conservation laws

  • J. Glimm, P. D. Lax
  • Mem. Amer. Math. Soc
  • 1970
Highly Influential
20 Excerpts

Hyperbolic systems of conservation laws II, Comm

  • P. D. Lax
  • Pure Appl. Math
  • 1957
Highly Influential
19 Excerpts

Souganidis, Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations

  • P.P.-L. Lions
  • Numer. Math
  • 1995
Highly Influential
5 Excerpts

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