The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V: Multidimensional Systems

Journal of Computational Physics

Volumn 141, Issue 2, 1998, Pages 199-224

  Cockburn, Bernardo ^a   Shu, Chi Wang ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b BROWN UNIVERSITY   (United States)

Author keywords

Discontinuous Galerkin; Euler equations; Slope limiters

Indexed keywords

COMPRESSIBILITY OF GASES; COMPUTATIONAL FLUID DYNAMICS; DEGREES OF FREEDOM (MECHANICS); GALERKIN METHODS; GAS DYNAMICS; PHYSICAL PROPERTIES; RUNGE KUTTA METHODS;

CONSERVATION LAW; DISCONTINUOUS GALERKIN; EULER'S EQUATION; HYPERBOLIC CONSERVATION LAWS; MULTIDIMENSIONAL SYSTEMS; NUMERICAL FLUX; QUADRATURE RULES; RUNGE-KUTTA DISCONTINUOUS GALERKIN METHODS; SLOPE LIMITER; SYSTEMS OF CONSERVATION LAWS;

EULER EQUATIONS;

EID: 0001690553     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.5892     Document Type: Article

References (37)

1. Atkins H. L., Shu C.-W. Quadrature-free Implementation of Discontinuous Galerkin Methods for Hyperbolic Equations. 1996.
2. Bar-Yoseph P. Space-time discontinuous finite element approximations for multi-dimensional nonlinear hyperbolic systems. Comput. Mech. 5:1989;145.
3. 2. Int. J. Numer. Methods Eng. 29:1990;1229.
4. F. Bassi, S. Rebay, High-order accurate discontinuous finite element solution of the 2D Euler equations, J. Comput. Phys.
5. Bassi F., Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131:1997;267.
6. Bazhenova S., Gvozdeva L., Nettleton M. Unsteady interactions of shock waves. Prog. Aerosp. Sci. 21:1984;249.
7. Berger M., Colella A. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82:1989;64.
8. Bey K. S., Oden J. T. A Runge-Kutta discontinuous Galerkin finite element method for high speed flows. AIAA 10th Computational Fluid Dynamics Conference. June 24-27, 1991.
9. Biswas R., Devine K. D., Flaherty J. Parallel, adaptive finite element methods for conservation laws. Applied Numerical Mathematics. 14:1994;255.
10. Carey G. F., Oden J. T. Finite Elements: Computational Aspects, III. 1984.
11. 2, AN, 23, 565, 1989.
12. Ciarlet P. The Finite Element Method for Elliptic Problems. 1975.
13. 2, AN, 25, 337, 1991.
14. Cockburn B., Shu C. W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: General framework. Math. Comp. 52:1989;411.
15. Cockburn B., Lin S. Y., Shu C. W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems. J. Comput. Phys. 84:1989;90.
16. Cockburn B., Hou S., Shu C. W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case. Math. Comp. 54:1990;545.
17. 1. 1991.
18. B. Cockburn, C. W. Shu, The local discontinuous Galerkin method for time-dependent convection diffusion systems, SIAM J. Numer. Anal.
19. deCougny H. L., Devine K. D., Flaherty J. E., Loy R. M., Özturan C., Shephard M. S. High-order accurate discontinuous discontinuous finite element solution of the 2D Euler equations. Applied Numerical Mathematics. 16:1994;157.
20. Devine K. D., Flaherty J. E., Loy R. M., Wheat S. R. Parallel Partitioning Strategies for the Adaptive Solution of Conservation Laws. 1994.
21. Devine K. D., Flaherty J. E., Wheat S. R., Maccabe A. B. A Massively Parallel Adaptive Finite Element Method with Dynamic Load Balancing. 1993.
22. Hillier R. Computation of shock wave diffraction at a ninety degrees convex edge. Shock Waves. 1:1991;89.
23. Hou S. A Finite Element Method for Conservation Laws: Multidimensional Case. 1991.
24. Jiang G., Shu C.-W. On cell entropy inequality for discontinuous Galerkin methods. Math. Comp. 62:1994;531.
25. Johnson C., Pitkäranta J. An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation. Math. Comp. 46:1986;1.
26. LeSaint P., Raviart P. A. On a finite element method for solving the neutron transport equation. 1974;89.
27. R. B. Lowrie, P. L. Roe, B. van Leer, Space-time discontinuous Galerkin: I. Theory and properties.
28. Özturan C., deCougny H. L., Shephard M. S., Flaherty J. E. Parallel adaptive mesh refinement and redistribution on distributed memory computers. Comput. Methods Appl. Mech. Engrg. 119:1994;123.
29. Peterson T. A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation. SIAM J. Numer. Anal. 28:1991;133.
30. Quirk J. A construction to the great Riemann solver debate. Int. J. Numer. Meth. Fluids. 18:1994;555.
31. Reed W. H., Hill T. R. Triangular Mesh Methods for the Neutron Transport Equation. 1973.
32. Richter G. R. An optimal-order error estimate for the discontinuous Galerkin method. Math. Comp. 50:1988;75.
33. Shu C.-W. TVB uniformly high-order schemes for conservation laws. Math. Comp. 49:1987;105.
34. Shu C.-W. Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9:1988;1073.
35. Shu C.-W., Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77:1988;439.
36. Shu C.-W., Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys. 83:1989;32.
37. Woodward P., Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54:1984;115.