Free Access
Issue
ESAIM: M2AN
Volume 49, Number 4, July-August 2015
Page(s) 1085 - 1126
DOI https://doi.org/10.1051/m2an/2015001
Published online 30 June 2015
  1. S. Adjerid, K. Devine, J. Flaherty and L. Krivodonova, A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems. Comput. Methods Appl. Mech. Engrg. 191 (2002) 1097–1112. [CrossRef] [MathSciNet] [Google Scholar]
  2. C. Agut, J. Diaz and A. Ezziani, High-order schemes combining the modified equation approach and discontinuous Galerkin approximations for the wave equation. Commun. Comput. Phys. 11 (2012) 691–708. [Google Scholar]
  3. M. Ainsworth, Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. J. Comput. Phys. 19 (2004) 106–130. [CrossRef] [Google Scholar]
  4. 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) 5–40. [CrossRef] [MathSciNet] [Google Scholar]
  5. P.F. Antonietti, I. Mazzieri, A. Quarteroni and F. Rapetti, Non-conforming high order approximations of the elastodynamics equation. Comput. Methods Appl. Mech. Engrg. 209–212 (2012) 212–238. [CrossRef] [Google Scholar]
  6. S. Aoi and H. Fujiwara, 3D Finite-difference method using discontinuous grids. Bull. Seism. Soc. Am. 89 (1999) 918–930. [Google Scholar]
  7. Z. Alterman and F.C. Karal, Propagation of elastic waves in layered media by finite-difference methods. Bull. Seism. Soc. Am. 58 (1968) 367–398. [Google Scholar]
  8. H. Bao, J. Bielak, O. Ghattas, L. Kallivokas, D.R. O’Hallaron, J.R. Schewchuk and J. Xu, Large-scale simulation of elastic wave propagation in heterogeneous media on parallel computers. Comput. Methods Appl. Mech. Engrg. 152 (1998) 85–102. [CrossRef] [Google Scholar]
  9. A. Bayliss, K.E. Jordan, B.J. LeMesurier and E. Turkel, A fourth-order accurate finite-difference scheme for the computation of elastic waves. Bull. Seism. Soc. Am. 76 (1986) 1115–1132. [Google Scholar]
  10. M. Benjemaa, Étude et simulation numérique de la rupture dynamique des séismes par des méthodes d’éléments finis discontinus. Ph.D. thesis, Nice-Sophia Antipolis University (2007). [Google Scholar]
  11. M. Benjemaa, S. Piperno and N. Glinsky-Olivier, Étude de stabilité d’un schéma volumes finis pour les équations de l’élasto-dynamique en maillages non structurés, INRIA report 5817 (2006). [Google Scholar]
  12. M. Bouchon and K. Aki, Discrete wave-number representation of seismic-source wave fields. Bull. Seism. Soc. Am. 67 (1977) 259–277. [Google Scholar]
  13. T. Bui-Thanh and O. Ghattas, Analysis of an hp-nonconforming discontinuous Galerkin spectral element method for wave propagation. SIAM J. Numer. Anal. 50 (2012) 1801–1826. [CrossRef] [Google Scholar]
  14. E. Chaljub, Y. Capdeville and J.P. Vilotte, Solving elastodynamics in a fluid–solid heterogeneous sphere: a parallel spectral element approximation on non–conforming grids. J. Comput. Phys. 187 (2003) 457–491. [CrossRef] [Google Scholar]
  15. Y. Cheng and C.-W. Shu, Superconvergence and time evolution of discontinuous Galerkin finite element solutions. J. Comput. Phys. 227 (2008) 9612–9627. [CrossRef] [Google Scholar]
  16. N. Chevaugeon, K. Hillewaert, X. Gallez, P. Ploumhans and J.-F. Remacle, Optimal numerical parameterization of discontinuous Galerkin method applied to wave propagation problems. J. Comput. Phys. 223 (2007) 188–207. [CrossRef] [Google Scholar]
  17. P. Ciarlet, The finite element method for elliptic problems. North Holland-Elsevier science publishers, Amsterdam, New York, Oxford (1978). [Google Scholar]
  18. B. Cockburn and C.W. Shu, TVB Runge−Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Math. Comput. 52 (1989) 411–435. [Google Scholar]
  19. B. Cockburn and C.W. Shu, The Runge−Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141 (1998) 199–224. [CrossRef] [MathSciNet] [Google Scholar]
  20. B. Cockburn, S.Y. Lin and C.W. Shu, TVB Runge−Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one dimensional systems. J. Comput. Phys. 84 (1989) 90–113. [CrossRef] [MathSciNet] [Google Scholar]
  21. B. Cockburn, S. Hou and C.W. Shu, The Runge−Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case. Math. Comput. 54 (1990) 545–581. [Google Scholar]
  22. B. Cockburn, G.E. Karnadiakis and C.W. Shu, Discontinuous Galerkin Methods: Theory, Computation and Application. Lect. Notes Comput. Sci. Engrg. Springer, Berlin (2000). [Google Scholar]
  23. J.D. De Basabe, M.K. Sen and M. Wheeler, The interior penalty discontinuous Galerkin method for elastic wave propagation: grid dispersion. Geophys. J. Int. 175 (2008) 83–93. [CrossRef] [Google Scholar]
  24. L. Demkowicz and J. Kurtz, Projection-based interpolation and automatic hp-adaptivity for finite element discretizations of elliptic and Maxwell problems. ESAIM: Proc. 21 (2007) 1–15. [CrossRef] [EDP Sciences] [Google Scholar]
  25. S. Delcourte, L. Fezoui and N. Glinsky-Olivier, A high-order Discontinuous Galerkin method for the seismic wave propagation. ESAIM Proc. 27 (2009) 70–89. [CrossRef] [EDP Sciences] [Google Scholar]
  26. M. Dumbser and M. Käser, An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes II: the three-dimensional isotropic case. Geophys. J. Int. 167 (2006) 319–336. [CrossRef] [Google Scholar]
  27. M. Dumbser, M. Käser and J. de la Puente, Arbitrary high order finite volume schemes for seismic wave propagation on unstructured meshes in 2D and 3D. Geophys. J. Int. 171 (2007) 665–694. [CrossRef] [Google Scholar]
  28. V. Etienne, E. Chaljub, J. Virieux and N. Glinsky, An hp-adaptive discontinuous Galerkin finite-element method for 3-D elastic wave modelling. Geophys. J. Int. 183 (2010) 941–962. [CrossRef] [Google Scholar]
  29. H. Fahs, High-order Leap-Frog based discontinuous Galerkin method for the time-domain Maxwell equations on non-conforming simplicial meshes. Numer. Math. Theor. Methods Appl. 2 (2009) 275–300. [Google Scholar]
  30. L. Fezoui, S. Lanteri, S. Lohrengel and S. Piperno, Convergence and stability of a Discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes. ESAIM: M2AN 39 (2005) 1149–1176. [CrossRef] [EDP Sciences] [Google Scholar]
  31. J.S. Hesthaven and T. Warburton, Nodal discontinuous Galerkin methods: algorithms, analysis and applications. Texts Appl. Math. 54 (2008). [CrossRef] [Google Scholar]
  32. F.Q. Hu, M.Y. Hussaini and P. Rasetarina, An analysis of the discontinuous Galerkin method for wave propagation problems. J. Comput. Phys. 151 (1999) 921–946. [CrossRef] [Google Scholar]
  33. M. Galis, P. Moczo and J. Kristek, A 3-D hybrid finite-difference–finite-element viscoelastic modelling of seismic wave motion. Geophys. J. Int. 175 (2008) 153–184. [CrossRef] [Google Scholar]
  34. D. Givoli, High-order local non-reflecting boundary conditions: a review. Wave Motion 39 (2004) 319–326. [CrossRef] [Google Scholar]
  35. N. Glinsky, S. Moto Mpong and S. Delcourte, A high-order discontinuous Galerkin scheme for elastic wave propagation. INRIA report No. 7476 (2010). [Google Scholar]
  36. C. Johnson and J. Pitkäranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equations. Math. Comput. 46 (1986) 1–26. [CrossRef] [MathSciNet] [Google Scholar]
  37. C. Johnson, U. Nävert and J. Pitkäranta, Finite element methods for linear hyperbolic equations. Comput. Methods Appl. Mech. Engrg. 45 (1984) 285–312,. [CrossRef] [MathSciNet] [Google Scholar]
  38. M. Käser and M. Dumbser, An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes I: the two-dimensional isotropic case with external source term. Geophys. J. Int. 162 (2006) 855–877. [CrossRef] [Google Scholar]
  39. M. Käser, M. Dumbser, J. de la Puente and H. Igel, An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes III: viscoelastic attenuation. Geophys. J. Int. 168 (2007) 224–242. [CrossRef] [Google Scholar]
  40. M. Käser, V. Hermann and J. de la Puente, Quantitative accuracy analysis of the discontinuous Galerkin method for seismic wave propagation. Geophys. J. Int. 173 (2008) 990–999,. [CrossRef] [Google Scholar]
  41. K.R. Kelly, R.W. Ward, S. Treitel and R.M. Alford, Synthetic seismograms: a finite-difference approach. Geophys. 41 (1976) 2–27. [CrossRef] [Google Scholar]
  42. D. Komatitsch and J.P. Vilotte, The spectral-element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures. Bull. Seism. Soc. Am. 88 (1998) 368–392. [Google Scholar]
  43. T. Lähivaara and T. Huttunen, A non-uniform basis order for the discontinuous Galerkin method of the acoustic and elastic wave equations. Appl. Numer. Math. 61 (2011) 473–486. [CrossRef] [Google Scholar]
  44. P. Lesaint and P.-A. Raviart, On a finite element method for solving the neutron transport equation, Mathematical Aspects of Finite Element Methods in Partial Differential Equations, edited by C.A. deBoor. Academic Press, New York (1974) 89–123. [Google Scholar]
  45. A.R. Levander, Fourth-order finite-difference P-SV seismograms. Geophys. 53 (1988) 1425–1436. [CrossRef] [Google Scholar]
  46. J. Lysmer and L.A. Drake, A finite element method for seismology, in Methods of Computational Physics, edited by B.A. Bolt. Academic Press, New York 11 (1972) 181–216. [Google Scholar]
  47. R. Madariaga, Dynamics of an expanding circular fault. Bull. Seis. Soc. Am. 66 (1976) 639–666. [Google Scholar]
  48. K.J. Marfurt, Accuracy of finite-difference and finite-element modelling of the scalar and elastic wave equations. Geophys. 49 (1984) 533–549. [CrossRef] [Google Scholar]
  49. I. Mazzieri and F. Rapetti, Dispersion analysis of triangle-based spectral elements methods for elastic wave propagation. Numer. Algorithms 60 (2012) 631–650. [CrossRef] [Google Scholar]
  50. E.D. Mercerat, J.-P. Vilotte and F. Sanchez-Sesma, Triangular spectral element simulation of 2D elastic wave propagation using unstructured triangular grids. Geophys. J. Int. 166 (2006) 679–698. [CrossRef] [Google Scholar]
  51. P. Moczo, E. Bystrický, J. Kristek, J.M. Carcione and M. Bouchon, Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures. Bull. Seism. Soc. Am. 87 (1997) 1305–1323. [Google Scholar]
  52. C. Pelties, J. de la Puente, J.P. Ampuero, G. Brietzke and M. Käser, Three-dimensional dynamic rupture simulations with a high-order discontinuous Galerkin method on unstructured tetrahedral meshes. J. Geophys. Res. 117 (2012) B02309. [Google Scholar]
  53. F. Peyrusse, N. Glinsky, C. Gélis and S. Lanteri, A nodal discontinuous Galerkin method for site effects assessment in viscoelastic media. Verification and validation in the Nice basin. Geophys. J. Int. (2014) 315–334. [Google Scholar]
  54. A. Pitarka, 3D elastic finite-difference modeling of seismic motion using staggered-grids with nonuniform spacing. Bull. Seism. Soc. Am. 89 (1999) 85–106. [Google Scholar]
  55. W. Reed and T. Hill, Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, NM (1973). [Google Scholar]
  56. C. Scheid and S. Lanteri, Convergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell’s equations in dispersive media. INRIA Report 7634 (2011). [Google Scholar]
  57. E.H. Saenger, N. Gold and S.A. Shapiro, Modeling the propagation of elastic waves using a modified finite-difference grid. Wave Motion 31 (2000) 77–92. [CrossRef] [Google Scholar]
  58. S. Sherwin, Dispersion analysis of the continuous and discontinuous Galerkin formulation. Lect. Notes Comput Sci. Engrg. 11 (2000) 425–432. [CrossRef] [Google Scholar]
  59. E. Süli, C. Schwab and P. Houston, hp-DGFEM for partial differential equations with non-negative characteristics form, in Discontinuous Galerkin Methods Theory. Computation and Applications, edited by B. Cockburn, G.E. Karnadiakis and C.W. Shu. In vol. 11 of Lect. Notes Comput. Sci. Eng. Springer, Berlin (2000) 221–230. [Google Scholar]
  60. J. Tago, V.M. Cruz-Atienza, J. Virieux, V. Etienne and F.J. Sanchez-Sesma, A 3D hp-adaptive discontinuous Galerkin method for modelling earthquake dynamics. J. Geophys. Research: Solid Earth 117 (2012). [Google Scholar]
  61. J. Virieux, P-SV wave propagation in heterogeneous media, velocity-stress finite difference method. Geophys. 51 (1986) 889–901. [CrossRef] [Google Scholar]
  62. J.L. Young, High-order, leapfrog methodology for the temporally dependent Maxwell’s equations. Radio Sci. 36 (2001) 9–17. [CrossRef] [Google Scholar]
  63. L.C. Wilcox, G. Stadler, C. Burstedde and O. Ghattas, A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media. J. Comput. Phys. 229 (2010) 9373–9396. [CrossRef] [Google Scholar]
  64. X. Zhong and C.-W. Shu, Numerical resolution of discontinuous Galerkin methods for time dependent wave equations. Comput. Methods Appl. Mech. Engrg. 200 (2011) 2814–2827. [CrossRef] [MathSciNet] [Google Scholar]

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