Free Access
Volume 54, Number 4, July-August 2020
Page(s) 1415 - 1428
Published online 18 June 2020
  1. G.Q. Chen and Y.G. Lu, The study on application way of the compensated compactness theory. Chin. Sci. Bull. 34 (1989) 15–19. [Google Scholar]
  2. T. Chen and C.-W. Shu, Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws. J. Comput. Phys. 345 (2017) 427–461. [Google Scholar]
  3. C.M. Dafermos, Hyperbolic conservation laws in continuum physics, 4th edition. In: Vol. 325 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (2016). [CrossRef] [Google Scholar]
  4. U.S. Fjordholm, High-order accurate entropy stable numerical schemes for hyperbolic conservation laws. , Ph.D. thesis, ETH Zurich, No. 21025. [Google Scholar]
  5. U.S. Fjordholm, Stability properties of the ENO method. Handbook of Numerical Methods for Hyperbolic Problems: Basic and Fundamental Issues. In: Vol. 17 of Handbook of Numerical Analysis. Elsevier (2016) 123–145. [Google Scholar]
  6. U.S. Fjordholm and S.H. Zakerzadeh, High-order accurate, fully discrete entropy stable schemes for scalar conservation laws. IMA J. Numer. Anal. 36 (2016) 633–654. [CrossRef] [Google Scholar]
  7. U.S. Fjordholm, S. Mishra and E. Tadmor, Arbitrarily high-order accurate entropy stable essentially nonoscillatory schemes for systems of conservation laws. SIAM J. Numer. Anal. 50 (2012) 544–573. [Google Scholar]
  8. U.S. Fjordholm, S. Mishra and E. Tadmor, ENO reconstruction and ENO interpolation are stable. Found. Comput. Math. 13 (2013) 139–159. [CrossRef] [Google Scholar]
  9. E. Godlewski and P.A. Raviart, Hyperbolic systems of conservation lawsIn: Vol. 3/4 of Mathématiques & Applications (Paris) [Mathematics and Applications]. Ellipses, Paris (1991). [Google Scholar]
  10. A. Harten, J.M. Hyman and P.D. Lax, On finite-difference approximations and entropy conditions for shocks. With an appendix by B. Keyfitz. Comm. Pure Appl. Math. 29 (1976) 297–322. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Harten, S. Osher, B. Engquist and S.R. Chakravarthy, Some results on uniformly high-order accurate essentially nonoscillatory schemes. Appl. Numer. Math. 2 (1986) 347–377. [Google Scholar]
  12. H. Holden and N.H. Risebro, Front Tracking for Hyperbolic Conservation Laws, 2nd ed. Springer-Verlag, Berlin Heidelberg (2015). [CrossRef] [Google Scholar]
  13. V. Jovanović and C. Rohde, Error estimates for finite volume approximations of classical solutions for nonlinear systems of hyperbolic balance laws. SIAM J. Numer. Anal. 43 (2006) 2423–2449. [Google Scholar]
  14. S.N. Kruzkov, First order quasilinear equations in several independent variables. Math USSR SB 10 (1970) 217–243. [CrossRef] [Google Scholar]
  15. P.G. Lefloch, J.M. Mercier and C. Rohde, Fully discrete, entropy conservative schemes of arbitrary order. SIAM J. Numer. Anal. 40 (2002) 1968–1992. [Google Scholar]
  16. R.J. LeVeque, Finite volume methods for hyperbolic problems, Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2002). [Google Scholar]
  17. S. Osher, Riemann solvers, the entropy condition, and difference approximations. SIAM J. Numer. Anal. 21 (1984) 217–235. [Google Scholar]
  18. E.Y. Panov, Existence and strong pre-compactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux. Arch. Ration. Mech. Anal. 195 (2010) 643–673. [Google Scholar]
  19. E. Tadmor, Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comput. 43 (1984) 369–381. [Google Scholar]
  20. E. Tadmor, The numerical viscosity of entropy stable schemes for systems of conservation laws I. Math. Comput. 49 (1987) 91–103. [Google Scholar]
  21. E. Tadmor, Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems. Acta Numer. 12 (2003) 451–512. [CrossRef] [MathSciNet] [Google Scholar]
  22. L. Tartar, Compensated compactness and applications to partial differential equations. In: Vol. 39 of Nonlinear Analysis and Mechanics: Heriot–Watt Symposium. Vol. IV, Notes in Math, Pitman, Boston, MA, London (1979) 136–212. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you