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All issues Volume 38 / No 6 (November-December 2004) ESAIM: M2AN, 38 6 (2004) 989-1009 References
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Issue
ESAIM: M2AN
Volume 38, Number 6, November-December 2004
Page(s) 989 - 1009
DOI https://doi.org/10.1051/m2an:2004047
Published online 15 December 2004
  1. F. Bouchut, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws. J. Statist. Phys. 95 (1999) 113–170. [Google Scholar]
  2. Y. Brenier, Average multivalued solutions for scalar conservation laws. SIAM J. Numer. Anal. 21 (1984) 1013–1037. [CrossRef] [MathSciNet] [Google Scholar]
  3. D.S. Butler, The numerical solution of hyperbolic systems of partial differential equations in three independent variables, in Proc. Roy. Soc. 255A (1960) 232–252. [Google Scholar]
  4. C. Cercignani, The Boltzmann equation and its applications. Springer-Verlag, New York (1988). [Google Scholar]
  5. R. Courant and D. Hilbert, Methods of Mathematical Physics II. Interscience Publishers, New York (1962). [Google Scholar]
  6. S.M. Deshpande, A second-order accurate kinetic-theory-based method for inviscid compressible flows. NASA Technical Paper 2613 (1986). [Google Scholar]
  7. H. Deconinck, P.L. Roe and R. Struijs, A multidimensional generalization of Roe's flux difference splitter for the Euler equations. Comput. Fluids 22 (1993) 215–222. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Fey, Ein echt mehrdimensionales Verfahren zur Lösung der Eulergleichungen. Dissertation, ETH Zürich, Switzerland (1993). [Google Scholar]
  9. M. Fey, Multidimensional upwinding. I. The method of transport for solving the Euler equations. J. Comput. Phys. 143 (1998) 159–180. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Fey, Multidimensional upwinding. II. Decomposition of the Euler equations into advection equations. J. Comput. Phys. 143 (1998) 181–199. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Fey, S. Noelle and C.v. Törne, The MoT-ICE: a new multi-dimensional wave-propagation-algorithm based on Fey's method of transport. With application to the Euler- and MHD-equations. Int. Ser. Numer. Math. 140, 141 (2001) 373–380. [Google Scholar]
  12. E. Godlewski and P.A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. Springer-Verlag, New York (1996). [Google Scholar]
  13. A. Jeffrey and T. Taniuti, Non-linear wave propagation. Academic Press, New York (1964). [Google Scholar]
  14. M. Junk, A kinetic approach to hyperbolic systems and the role of higher order entropies. Int. Ser. Numer. Math. 140, 141 (2001) 583–592. [Google Scholar]
  15. M. Junk and J. Struckmeier, Consistency analysis of mesh-free methods for conservation laws, Mitt. Ges. Angew. Math. Mech. 24, No. 2, 99 (2001). [Google Scholar]
  16. T. Kröger, Multidimensional systems of hyperbolic conservation laws, numerical schemes, and characteristic theory. Dissertation, RWTH Aachen, Germany (2004). [Google Scholar]
  17. T. Kröger and S. Noelle, Numerical comparison of the method of transport to a standard scheme. Comp. Fluids (2004) (doi: 10.1016/j.compfluid.2003.12.002) (in print). [Google Scholar]
  18. D. Kröner, Numerical schemes for conservation laws. Wiley Teubner, Stuttgart (1997). [Google Scholar]
  19. R.J. LeVeque, Numerical methods for conservation laws. Birkhäuser, Basel (1990). [Google Scholar]
  20. P. Lin, K.W. Morton and E. Süli, Characteristic Galerkin schemes for scalar conservation laws in two and three space dimensions. SIAM J. Numer. Anal. 34 (1997) 779–796. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. Lukáčová-Medviďová, K.W. Morton and G. Warnecke, Evolution Galerkin methods for hyperbolic systems in two space dimensions. Math. Comp. 69 (2000) 1355–1384. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Lukáčová-Medviďová, K.W. Morton and G. Warnecke, Finite volume evolution Galerkin (FVEG) methods hyperbolic systems. SIAM J. Sci. Comp. 26 (2004) 1–30. [CrossRef] [Google Scholar]
  23. M. Lukáčová-Medviďová, J. Saibertová and G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems. J. Comp. Phys. 183 (2002) 533–562. [Google Scholar]
  24. S. Noelle, The MoT-ICE: a new high-resolution wave-propagation algorithm for multidimensional systems of conservation laws based on Fey's Method of Transport. J. Comput. Phys. 164 (2000) 283–334. [CrossRef] [MathSciNet] [Google Scholar]
  25. S. Ostkamp, Multidimensional Characteristic Galerkin Schemes and Evolution Operators for Hyperbolic Systems. Dissertation, Hannover University, Germany (1995). [Google Scholar]
  26. S. Ostkamp, Multidimensional characteristic Galerkin methods for hyperbolic systems. Math. Meth. Appl. Sci. 20 (1997) 1111–1125. [CrossRef] [Google Scholar]
  27. B. Perthame, Boltzmann type schemes for gas dynamics and the entropy property. SIAM J. Numer. Anal. 27 (1990) 1405–1421. [CrossRef] [MathSciNet] [Google Scholar]
  28. B. Perthame, Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions. SIAM J. Numer. Anal. 29 (1992) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  29. P. Prasad, Nonlinear hyperbolic waves in multi-dimensions. Chapman & Hall/CRC, New York (2001). [Google Scholar]
  30. J. Quirk, A contribution to the great Riemann solver debate. Int. J. Numer. Meth. Fluids 18 (1994) 555–574. [Google Scholar]
  31. P. Roe, Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics. J. Comput. Phys. 63 (1986) 458–476. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  32. J.L. Steger and R.F. Warming, Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. J. Comput. Phys. 40 (1981) 263–293. [CrossRef] [MathSciNet] [Google Scholar]
  33. C.v. Törne, MOTICE – Adaptive, Parallel Numerical Solution of Hyperbolic Conservation Laws. Dissertation, Bonn University, Germany. Bonner Mathematische Schriften, No. 334 (2000). [Google Scholar]
  34. E. Toro, Riemann solvers and numerical methods for fluid dynamics. Second edition, Springer, Berlin (1999). [Google Scholar]
  35. K. Xu, Gas-kinetic schemes for unsteady compressible flow simulations. Lect. Ser. Comp. Fluid Dynamics, VKI report 1998-03 (1998). [Google Scholar]
  36. S. Zimmermann, The method of transport for the Euler equations written as a kinetic scheme. Int. Ser. Numer. Math. 141 (2001) 999–1008. [Google Scholar]
  37. S. Zimmermann, Properties of the Method of Transport for the Euler Equations. Dissertation, ETH Zürich, Switzerland (2001). [Google Scholar]

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