Open Access
Volume 57, Number 2, March-April 2023
Page(s) 395 - 422
Published online 03 March 2023
  1. T. Barth and D.C. Jespersen, The design and application of upwind schemes on unstructured meshes. American Institute for Aeronautics and Astronautics, Report 89-0366:1-12 (1989). [Google Scholar]
  2. T. Barth, R. Herbin and M. Ohlberger, Finite Volume Methods: Foundation and Analysis. Encyclopedia of Computational Mechanics, John Wiley & Sons (2017). [Google Scholar]
  3. J. Bernier, F. Casas and N. Crouseilles, Splitting methods for rotations: application to Vlasov equations. SIAM J. Sci. Comput. 42 (2020) A666–A697. [CrossRef] [Google Scholar]
  4. F. Bonnans, G. Bonnet and J.-M. Mirebeau, Second order monotone finite differences discretization of linear anisotropic differential operators. Math. Comput. Am. Math. Soc. 90 (2021) 2671–2703. [Google Scholar]
  5. F. Bouchut, F. James and S. Mancini, Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient. Ann. Sc. Norm. Super. Pisa Cl. Sci. 4 (2005) 1–25. [MathSciNet] [Google Scholar]
  6. W. Cao, C.-W. Shu, Y. Yang and Z. Zang, Superconvergence of discontinuous Galerkin method for linear hyperbolic equations in one space dimension. SIAM J. Numer. Anal. 56 (2018) 732–765. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Chainais-Hillairet, Second-order finite-volume schemes for a non-linear hyperbolic equation: error estimate. Math. Methods Appl. Sci. 23 (2000) 467–490. [Google Scholar]
  8. N. Crouseilles, M. Mehrenberger and E. Sonnendrucker, Conservative semi-Lagrangian schemes for Vlasov equations. J. Comput. Phys. 229 (2010) 1927–1953. [CrossRef] [MathSciNet] [Google Scholar]
  9. B. Després, Numerical Methods for Eulerian and Lagrangian Conservation Laws. Springer Verlag (2017). [CrossRef] [Google Scholar]
  10. B. Després, Lax theorem and finite volume schemes. Math. Comp. 73 (2003) 1203–1234. [CrossRef] [Google Scholar]
  11. B. Despres, Uniform asymptotic stability of Strang’s explicit compact schemes for linear advection. SIAM J. Numer. Anal. 47 (2009) 3956–3976. [CrossRef] [MathSciNet] [Google Scholar]
  12. B. Després, F. Lagoutière, Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids. M2AN Math. Model. Numer. Anal. 35 (2001) 1159–1183. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  13. B. Després and F. Lagoutière, A longitudinal variation diminishing estimate for linear advection on arbitrary grids. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 259–263. [CrossRef] [MathSciNet] [Google Scholar]
  14. L. Einkemmer and A. Ostermann, Convergence analysis of a discontinuous Galerkin/Strang splitting approximation for the Vlasov-Poisson equations. SIAM J. Numer. Anal. 52 (2014) 757–778. [CrossRef] [MathSciNet] [Google Scholar]
  15. R. Eymard, T. Gallouet, M. Ghilani and R. Herbin, Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes. IMA J. Numer. Anal. 18 (1998) 563–594. [CrossRef] [MathSciNet] [Google Scholar]
  16. R. Eymard, T. Gallouet and R. Herbin, Finite volume methods. Handbook Num. Anal. 7 (2000) 713–1020. [CrossRef] [Google Scholar]
  17. F. Filbet and E. Sonnendrücker, Comparison of Eulerian Vlasov solvers. Comput. Phys. Comm. 150 (2003) 247–266. [CrossRef] [MathSciNet] [Google Scholar]
  18. E. Godlewski and P.-A. Raviart, Hyperbolic systems of conservation laws, in Mathematics and Applications 3/4, Ellipses, Paris (1991). [Google Scholar]
  19. E. Godlewski and P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Applied Mathematical Sciences. Vol. 118. Springer (1996). [CrossRef] [Google Scholar]
  20. S. Godunov, A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations. Mat. Sbornik 47 (1959) 271–306. Translated US Joint Publ. Res. Service, JPRS 7226. [Google Scholar]
  21. J. Goodman and R.J. LeVeque, On the accuracy of stable schemes for 2D scalar conservation laws. Math. Comp. 45 (1985) 15–21. [CrossRef] [MathSciNet] [Google Scholar]
  22. J.-L. Guermond, B. Popov and J. Ragusa, Positive and asymptotic preserving approximation of the radiation transport equation. SIAM J. Numer. Anal. 58 (2020) 519–540. [CrossRef] [MathSciNet] [Google Scholar]
  23. J.-L. Guermond, M. Maier, B. Popov and I. Tomas, Second-order invariant domain preserving approximation of the compressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 375 (2021) 113608. [CrossRef] [Google Scholar]
  24. F. Haider, J.-P. Croisille and B. Courbet, Stability analysis of the cell centered finite-volume muscl method on unstructured grids. Numer. Math. 113 (2009) 555–600. [CrossRef] [MathSciNet] [Google Scholar]
  25. A. Harten, High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49 (1983) 357–393. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Harten, J.M. Hyman and P.D. Lax with appendix by B. Keyfitz, On finite-difference approximations and entropy conditions for shocks. Comm. Pure Appl. Math. 29 (1976) 297–322. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Kurganov, Y. Liu and V. Zeitlin, Numerical dissipation switch for two-dimensional central-upwind schemes. ESAIM: Math. Modell. Numer. Anal. 55 (2021) 713–734. [CrossRef] [EDP Sciences] [Google Scholar]
  28. G. Latu, M. Mehrenberger, Y. Guclu, M. Ottaviani and E. Sonnendrucker, Field-aligned interpolation for semi-Lagrangian gyrokinetic simulations. J. Sci. Comput. 74 (2018) 1601–1650. [CrossRef] [MathSciNet] [Google Scholar]
  29. R.J. Leveque, Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge (2012). [Google Scholar]
  30. J. Lu, Y. Liu and C.-W. Shu, An oscillation-free discontinuous Galerkin method for scalar hyperbolic conservation laws. SIAM J. Numer. Anal. 59 (2021) 1299–1324. [CrossRef] [MathSciNet] [Google Scholar]
  31. S. Osher and S. Chakravarthy, High resolution schemes and the entropy condition. SIAM J. Numer. Anal. 21 (1984) 955–984. [CrossRef] [MathSciNet] [Google Scholar]
  32. P.L. Roe and D. Sidilkover, Optimum positive linear schemes for advection in two and three dimensions. SIAM J. Numer. Anal. 29 (1992) 1542–1568. [CrossRef] [MathSciNet] [Google Scholar]
  33. C.-W. Shu, Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations. in Finite Volumes for Complex Applications VIII. Vol. 199. Springer (2017) 3–14. [Google Scholar]
  34. P.K. Sweby, High resolution schemes using flux-limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21 (1984) 995–1011. [CrossRef] [MathSciNet] [Google Scholar]
  35. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics – A Practical Introduction. Springer (2009). [CrossRef] [Google Scholar]
  36. X. Zhang and C.-W. Shu, Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments. Proc. R. Soc. 467 (2001) 2752–2776. [Google Scholar]

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