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Dispersion analysis of discontinuous Galerkin schemes applied to Poincare, Kelvin and Rossby waves

  1. Adjerid, S., Devine, K.D., Flaherty, J.E., Krivodonova, L.: A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems. Comput. Methods Appl. Mech. Eng. 191, 1097–1112 (2002)
  2. Ainsworth, M.: Dispersive and dissipative behavior of high order Discontinuous Galerkin finite element methods. J. Comput. Phys. 198(1), 106–130 (2004)
  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. 130, 267–279 (1997)
  4. Bassi, F., Rebay, S.: A high-order accurate discontinuous finite element solution of the 2D Euler equations. J. Comput. Phys. 138, 251–285 (1997)
  5. Beckers, J.-M., Deleersnijder, E.: Stability of a FBTCS scheme applied to the propagation of shallow-water inertia-gravity waves on various space grids. J. Comput. Phys. 108, 95–104 (1993)
  6. Bernard, P.-E., Chevaugeon, N., Legat, V., Deleersnijder, E., Remacle, J.-F.: High-order h-adaptive discontinuous Galerkin methods for ocean modeling. Ocean Dyn. 57, 109–121 (2007)
  7. Chevaugeon, N., Remacle, J.-F., Galler, X., Ploumans, P., Caro, S.: Efficient discontinuous Galerkin methods for solving acoustic problems. In: 11th AIAA/CEAS Aeroacoustics Conference (2005)
  8. Discontinuous Galerkin Methods, ISBN:9783642640988, 10.1007/978-3-642-59721-3
  9. Gavrilov, M.B., Tosic, I.A.: Propagation of the Rossby waves on two dimensional rectangular grids. Meteorol. Atmospheric Phys. 68, 119–125 (1998)
  10. Gottlieb, D., Hesthaven, J.: Spectral methods for hyperbolic problems. J. Comput. Appl. Math. 128, 83–131 (2001)
  11. Hanert, E., Le Roux, D.Y., Legat, V., Deleersnijder, E.: Advection schemes for unstructured grid ocean modelling. Ocean Model. 7, 39–58 (2004)
  12. Hu, F., Atkins, H.: Eigensolution analysis of the discontinuous Galerkin method with nonuniform grids I. One space dimension. J. Comput. Phys. 182(2), 516–545 (2002)
  13. Ihlenburg, F., Babuška, I.: Finite element solution of the Helmholtz equation with high wave number. Part 2. The h–p version of the finite element method. SIAM J. Numer. Anal. 34, 315–358 (1997)
  14. Iskandarani, M., Haidvogel, D.B., Boyd, J.P.: A staggered spectral element model with application to the oceanic shallow water equations. Int. J. Numer. Methods Fluids 20, 393–414 (1995)
  15. Longuet-Higgins, M.S.: Planetary waves on a rotating sphere II. Proc. R. Soc. Lond. 284, 40–68 (1965)
  16. Majda, A.: Introduction to PDE’s and Waves for the Atmosphere and Ocean. American Mathematical Society (2003)
  17. Marchandise, E., Chevaugeon, N., Remacle, J.-F.: Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems. J. Comput. Appl. Math. (2006, in press)
  18. Mesinger, F., Arakawa, A.: Numerical methods used in atmospheric models. Glob. Atmospheric Res. Programme (GARP) Publications Series No.17(1) (1976)
  19. Pietrzak, J., Deleersnijder, E., Schroeter, J. (eds.): Ocean Model. (special issue) 10, 1–252 (2005). The Second International Workshop on Unstructured Mesh Numerical Modelling of Coastal, Shelf and Ocean Flows (Delft, the Netherlands, September 23–25, 2003)
  20. Remacle, J.-F., Li, X., Shephard, M.S., Flaherty, J.E.: Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods. Int. J. Numer. Methods Eng. 62(7), 899–923 (2005)
  21. Thompson, L., Pinsky, P.: Complex wavenumber Fourier analysis of the p-version finite element method. Comput. Mech. 13, 255–275 (1994)
  22. Warburton, T., Karniadakis, G.E.: A discontinuous Galerkin method for the viscous MHD equations. J. Comput. Phys. 152, 608–641 (1999)
  23. Wentzel, G.: A generalization of quantum conditions for the purposes of wave mechanics. Z. Phys. 38, 518 (1926)
Bibliographic reference Bernard, Paul-Emile ; Deleersnijder, Eric ; Legat, Vincent ; Remacle, Jean-François. Dispersion analysis of discontinuous Galerkin schemes applied to Poincare, Kelvin and Rossby waves. In: Journal of Scientific Computing, Vol. 34, no. 1, p. 26-47 (2008)
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