Discontinuous Galerkin finite element method for the wave equation

SIAM Journal on Numerical Analysis

Volumn 44, Issue 6, 2006, Pages 2408-2431

  Grote, Marcus J ^a   Schneebeli, Anna ^a   Schötzau, Dominik ^b  

^a UNIVERSITY OF BASEL   (Switzerland)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

A priori error analysis; Acoustic waves; Discontinuous Galerkin finite element methods; Explicit time integration; Second order hyperbolic problems; Wave equation

Indexed keywords

ACOUSTIC WAVES; ERROR ANALYSIS; FINITE ELEMENT METHOD; WAVE EQUATIONS;

A PRIORI ERROR ANALYSIS; DISCONTINUOUS GALERKIN FINITE ELEMENT METHODS; SECOND-ORDER HYPERBOLIC PROBLEMS;

GALERKIN METHODS;

EID: 37849013422     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/05063194X     Document Type: Article

References (21)

1. M. AINSWORTH, P. MONK, AND W. MUNIZ, Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second order wave equation, J. Sci. Comput., 27 (2006), pp. 5-40.
2. D. N. ARNOLD, F. BREZZI, B. COCKBURN, AND L. D. MARINI, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal., 39 (2002), pp. 1749-1779.
3. G. A. BAKER, Error estimates for finite element methods for second order hyperbolic equations, SIAM J. Numer. Anal., 13 (1976), pp. 564-576.
4. W. BANGERTH, R. HARTMANN, AND G. KANSCHAT, deal.II Differential Equations Analysis Library, Technical Reference, IWR, Universität Heidelberg, Heidelberg, Germany, http://www.dealii.org.
5. W. BANGERTH AND G. KANSCHAT, Concepts for Object-Oriented Finite Element Software - The deal.II Library, Report 99-43, Sonderforschungsbereich 3-59, IWR, Universität Heidelberg, Heidelberg, Germany, 1999.
6. P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
7. B. COCKBURN, Discontinuous Galerkin methods for convection-dominated problems, in High-Order Methods for Computational Physics, Lect. Notes Comput. Sci. Eng. 9, T. Barth and H. Deconink, eds., Springer-Verlag, Berlin, 1999, pp. 69-224.
8. B. COCKBURN, G. E. KARNIADAKIS, AND C.-W. SHU, The development of discontinuous Galerkin methods, in Discontinuous Galerkin Methods: Theory, Computation and Applications, Lect. Notes Comput. Sei. Eng. 11, B. Cockburn, G. E. Karniadakis, and C.-W. Shu, eds., Springer-Verlag, Berlin, 2000, pp. 3-50.
9. B. COCKBURN AND C-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin method for conservation laws. II: General framework, Math. Comp., 52 (1989), pp. 411-435.
10. B. COCKBURN AND C.-W. SHU, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, J. Sci. Comput., 16 (2001), pp. 173-261.
11. G. COHEN, P. JOLY, J. E. ROBERTS, AND N. TORDJMAN, Higher order triangular finite elements with mass lumping for the wave equation, SIAM J. Numer. Anal., 38 (2001), pp. 2047-2078.
12. R. S. FALK AND G. R. RICHTER, Explicit finite element methods for symmetric hyperbolic equations, SIAM J. Numer. Anal., 36 (1999), pp. 935-952.
13. J. S. HESTHAVEN AND T. WARBURTON, Nodal high-order methods on unstructured grids. I. Time-domain solution of Maxwell's equations, J. Comput. Phys., 181 (2002), pp. 186-221.
14. P. HOUSTON, M. JENSEN, AND E. SÜLI, hp-discontinuous Galerkin finite element methods with least-squares stabilization, J. Sei. Comput., 17 (2002), pp. 3-25.
15. T. HUGHES, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987.
16. J.-L. LIONS AND E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications, Vol. I, Springer-Verlag, New York, 1972.
17. P. MONK AND G. R. RICHTER, A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media, J. Sci. Comput., 22-23 (2005), pp. 443-477.
18. I. PERUGIA AND D. SCHÖTZAU, An hp-analysis of the local discontinuous Galerkin method for diffusion problems, J. Sei. Comput., 17 (2002), pp. 561-571.
19. P. A. RAVIART AND J.-M. THOMAS, Introduction à l'Analyse Numérique des Équations aux Dérivées Partielles, Masson, Paris, 1983.
20. B. RIVIÈRE AND M. F. WHEELER, Discontinuous Finite Element Methods for Acoustic and Elastic Wave Problems, I: Semidiscrete Error Estimates, Technical report 01-02, TICAM, University of Texas, Austin, TX, 2001.
21. B. RIVIÈRE AND M. F. WHEELER, Discontinuous finite element methods for acoustic and elastic wave problems, in ICM2002-Beijing Satellite Conference on Scientific Computing, Contemp. Math. 329, AMS, Providence, RI, 2003, pp. 271-282.