An Analysis of the Discontinuous Galerkin Method for Wave Propagation Problems

Journal of Computational Physics

Volumn 151, Issue 2, 1999, Pages 921-946

  Hu, Fang Q ^a   Hussaini, M Y ^b   Rasetarinera, Patrick ^b  

^a OLD DOMINION UNIVERSITY   (United States)

^b FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Discontinuous Galerkin method; Dissipation, dispersion and anisotropy errors; Wave propagation

Indexed keywords

ADVECTION; GALERKIN METHODS; WAVE PROPAGATION;

ADVECTION EQUATIONS; DISCONTINOUS GALERKIN METHODS; DISSIPATION, DISPERSION AND ANISOTROPY ERROR; ONE-DIMENSIONAL; PROPERTY; SCALAR ADVECTION; SIMULATING WAVES; TRIANGULAR AND QUADRILATERAL ELEMENTS; TWO-DIMENSIONAL WAVE EQUATION; WAVE PROPAGATION PROBLEMS;

DISPERSION (WAVES);

EID: 0000458188     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6227     Document Type: Article

References (36)

1. Abboud N. N., Pinsky P. M. Finite-element dispersion analysis for the 3-dimensional 2nd-order scalar wave-equation. Int. J. Numer. Methods Eng. 35:1992;1183.
2. Atkins H. L., Shu C.-W. Quadrature-Free Implementation of Discontinuous Galerkin Method for Hyperbolic Equations. 1996.
3. 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.
4. Bey K. S., Oden J. T. h-p. Comput. Methods Appl. Mech. Eng. 133:1996;259.
5. Biswas R., Devine K. D., Flaherty J. Parallel, adaptive finite element methods for conservation laws. Appl. Numer. Math. 14:1994;255.
6. Bossavit A. A rationale for "edge elements" in 3-D fields computations. IEEE Trans. Mag. 24:1988;74.
7. 1. RAIRO, Model. Math. Anal. Numer. 23:1989;565.
8. Chaffin D. J., Baker A. J. On Taylor weak statement finite-element methods for computational fluid dynamics. Int. J. Numer. Methods Fluids. 21:1995;273.
9. 1. RAIRO, Model. Math. Anal. Numer. 25:1991;337.
10. Cockburn B., Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework. Math. Comput. 52:1989;411.
11. 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.
12. 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. Comput. 54:1990;545.
13. Cockburn B., Shu C.-W. The Runge-Kutta discontinuous Galerkin finite-element method for conservation laws. V. Multidimensional systems. J. Comput. Phys. 141:1998;199.
14. Cockburn B., Shu C.-W. The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems. 1997.
15. Godunov S. K. Finite difference method for numerical computation of discontinuous solutions of fluid dynamics. Math. Sbornik. 47:1959;251.
16. Hu F. Q., Hussaini M. Y., Manthey J. L. Application of low dissipation and dispersion Runge-Kutta schemes to benchmark problems in computational aeroacoustics. Proceedings, ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics, Hampton, Virginia, October 1994. 1995.
17. Hu F. Q., Hussaini M. Y., Manthey J. L. Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics. J. Comput. Phys. 124:1996;177.
18. Khelifa A., Ouellet Y. Analysis of time-varying errors in quadratic finite-element approximation of hyperbolic problems. Int. J. Numer. Methods Eng. 38:1995;3933.
19. Johnson C., Pitk\"aranta J. An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation. Math. Comput. 46:1986;1.
20. Lele S. K. Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103:1992;16.
21. Lesaint P., Raviart P. A. On a finite element method for solving the neutron transport equation. Mathematical Aspects of Finite Elements in Partial Differential Equations. 1974;89.
22. Liu Y. Fourier analysis of numerical algorithms for the Maxwell equations. J. Comput. Phys. 124:1996;396.
23. Lowrie R. B. Compact Higher-Order Numerical Methods for Hyperbolic Conservation Laws. 1996.
24. Lowrie R. B., Roe P. L., Van Leer B. A Space-Time Discontinuous Galerkin Method for the Time-Accurate Numerical Solution of Hyperbolic Conservation Laws. 1995.
25. Makridakis C., Monk P. Time-discrete finite element schemes for Maxwell's equations. RAIRO, Model. Math. Anal. Numer. 29:1995;171.
26. Mur G. The finite-element modeling of three-dimensional time-domain electromagnetic fields in strongly inhomogeneous media. IEEE Trans. Mag. 28:1992;1130.
27. Peterson T. A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation. SIAM J. Numer. Anal. 28:1991;133.
28. Reed W. H., Hill T. R. Triangular Mesh Methods for the Neutron Transport Equation. 1973.
29. Richter G. R. An optimal-order error estimate for the discontinuous Galerkin method. Math. Comput. 50:1988;75.
30. Shakib F., Hughes T. J. R. A new finite element formulation for computational fluid dynamics. IX. Fourier analysis of space-time Galerkin/least-squares algorithms. Comput. Methods Appl. Mech. Eng. 87:1991;35.
31. Shang J. S. High-Order Compact-Difference Schemes for Time-Dependent Maxwell Equations. 1998.
32. Steger J., Warming R. F. Flux vector splitting of the inviscid gas-dynamic equations with applications to the finite difference methods. J. Comput. Phys. 40:1981;263.
33. Tam C. K. W., Webb J. W. Dispersion-relation-preserving finite difference schemes for computational acoustics. J. Comput. Phys. 107:1993;262.
34. Thompson L. L., Pinsky P. M. Complex wave-number Fourier-analysis of the p-version finite element method. Comput. Mech. 13:1994;255.
35. Waburton T. C., Lomtev I., Kirby R. M., Karniadakis G. A Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on hybrid grids. 1997.
36. Wu J. Y., Lee R. The advantages of triangular and tetrahedral edge elements for electromagnectic modeling with the finite-element method. IEEE Trans. Antennas and Propagation. 45:1997;1431.