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Journal of parallel and distributed computing

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Unformatted text preview: the large for nonlinear hyperbolic systems of equations. Communications on Pure and Applied Mathematics, 18:697{715, 1965. 18] S.K. Godunov. A nite di erence method for the numerical computation of discontinuous solutions of the equations of uid dynamics. Mat. Sbornik., 47:271{306, 1959. 19] C. Johnson. Error estimates and adaptive time step control for a class of one step methods for sti ordinary di erential equations. SIAM Journal on Numerical Analysis, 25:908{926, 1988. 20] P.D. Lax. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves. Regional Conference Series in Applied Mathematics, No. 11. SIAM, Philadelphia, 1973. 10.3. Multidimensional Discontinuous Galerkin Methods 43 21] W.H. Reed and T.R. Hill. Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scienti c Laboratory, Los Alamos, 1973. 22] J.-F. Remacle, J.E. Flaherty, and M.S. Shephard. Adaptive order discontinuous galerkin methods. In preparation, 2000. 23] P.L. Roe. Approximate Riemann solvers, parameter vectors, and di erence schemes. Journal of Computational Physics, 43:357{372, 1981. 24] P. Le Saint and P. Raviart. On a nite element method for solving the newtron transport equations. In C. de Boor, editor, Mathematical Aspects of Finite Elements in Partial Di erential Equations, pages 89{145, New York, 1974. Academic Press. 25] G.A. Sod. Numerical Methods in Fluid Dynamic. Cambridge University Press, Cambridge, 1985. 26] J.L Steger and R.F. Warming. Flux vector splitting of the inviscid gasdynamic equations with applications to nite di erence methods. Journal of Computational Physics, 40:263{293, 1981. 27] B. van Leer. Flux-vector splitting gor the Euler equations. Lecture Notes in Physics, 170:507{512, 1982. 28] M.F. Wheeler. An elliptic collocation- nite element method with interior penalties. SIAM Journal on Numerical Analysis, 15:152{161, 1978....
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