Dispersive and dissipative properties of discontinuous galerkin Finite element methods for the second-order wave equation

Journal of Scientific Computing

Volumn 27, Issue 1-3, 2006, Pages 5-40

  Ainsworth, M ^a   Monk, P ^b   Muniz, W ^b  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b UNIVERSITY OF DELAWARE   (United States)

Author keywords

Discontinuous Galerkin finite element method; Numerical dispersion; Numerical dissipation; Wave propagation

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; DISPERSION (WAVES); ENERGY DISSIPATION; MAXWELL EQUATIONS; TIME DOMAIN ANALYSIS;

DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD; NUMERICAL DISPERSION; NUMERICAL DISSIPATION; TIME DOMAIN SIMULATION;

WAVE EQUATIONS;

EID: 33745044014     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-005-9044-x     Document Type: Conference Paper

References (20)

1. Ainsworth, M. (2004). Discrete dispersion relation for hp-version finite element approximation at high wave number. SIAM J. Numer. Anal. 42(2), 553-575.
2. Ainsworth, M. (2004). Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. J. Comp. Phys. 198, 106-130.
3. Arnold, D. N. (1982). An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19, 742-760.
4. Arnold, D. N., Brezzi, F., Cockburn, B., and Marini, L. D. (2002). Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749-1779.
5. Baker, G. A. (1977). Finite element methods for elliptic equations using non-conforming elements. Math. Comput. 31, 45-59.
6. Cockburn, B. (2003). Discontinuous Galerkin methods. ZAMM Z. Angew. Math. Mech. 83, 731-754.
7. Cockburn, B., Karniadakis, G., and Shu, C. W. (eds.), (2000). First International Symposium on Discontinuous Galerkin methods, volume 11 of Lecture notes in Computational Science and Engineering. Springer.
8. Cockburn, B., and Shu, C.-W. (1998). The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35, 2440-2463.
9. Cockburn, B., and Shu, C.-W (2001). Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. SIAM J. Sci. Comput. 16, 193-261.
10. Cohen, G. C. (2002). Higher-order Numerical Methods far Transient Wave Equations. Springer, Berlin.
11. Douglas, J., and Dupont, T. (1976). Interior Penalty Procedures for Elliptic and Hyperbolic Discontinuous Galerkin Procedures, volume 58 of Lecture notes in physics. Springer-Verlag.
12. Hesthaven, J. S., and Warburton, T. (2002). Nodal high-order methods on unstructured grids - I. Time-domain solution of Maxwell's equations. J. Comput. Phys. 181, 186-221.
13. Hu, F. Q., and Atkins, H. L. (2002). Eigensolution analysis of the discontinuous Galerkin method with non-uniform grids. Part 1: One space dimension. J. Comput. Phys. 182(2), 516-545.
14. Hu, F. Q., and Atkins, H. L. (2002). Two-dimensional wave analysis of the discontinuous Galerkin method with non-uniform grids and boundary conditions. In Proc. 8th AIAA/CEAS Aeronautics Conference, Breckenridge, Colorado, June 2002. AIAA paper no. 2002-2514.
15. Odeh, F., and Keller, J. B. (1964). Partial differential equations with periodic coefficients and Bloch waves in crystals. J. Math. Phys. 5, 1499-504.
16. Reed, W. H., and Hill, T. R. (1973). Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos National Laboratory, Los Alamos, New Mexico, USA.
17. Riviere, B., and Wheeler, M. (2003). Discontinuous finite element methods for acoustic and elastic wave problem. In ICM2002-Beijing Satellite Conference on Scientific Computing, volume 329 of Contemporary Mathematics, AMS, pp. 271-282.
18. Vichnevetsky, R., and Bowles, J. B. (1982). Fourier Analysis of Numerical Approximations of Hyperbolic Equations, volume 5 of CMBS Regional Conference Series in Applied Mathematics. SIAM, Philadelphia.
19. Vila, J.-P., and Villedieu, P. (2003). Convergence of an explicit finite volume scheme for first order symmetric systems. Numer. Math. 94, 573-602.
20. Wheeler, M. F. (1978). An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15, 152-161.