Dispersion Analysis of HDG Methods (original) (raw)

Access this article

Log in via an institution

Subscribe and save

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Ainsworth, M.: Discrete dispersion relation for \(hp\)-version finite element approximation at high wave number. SIAM J. Numer. Anal. 42(2), 553–575 (2004)
    Article MathSciNet Google Scholar
  2. Ainsworth, M.: Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. J. Comput. Phys. 198(1), 106–130 (2004)
    Article MathSciNet Google Scholar
  3. Ainsworth, M., Monk, P., Muniz, W.: Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second order wave equation. J. Sci. Comput. 27(1–3), 5–40 (2006)
    Article MathSciNet Google Scholar
  4. Babuška, I.M., Sauter, S.A.: Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? SIAM J. Numer. Anal. 34(6), 2392–2423 (1997)
    Article MathSciNet Google Scholar
  5. Chung, E., Cockburn, B., Fu, G.: The staggered DG method is the limit of a hybridizable DG method. SIAM J. Numer. Anal. 52(2), 915–932 (2014)
    Article MathSciNet Google Scholar
  6. Chung, E., Engquist, B.: Optimal discontinuous Galerkin methods for the acoustic wave equation in higher dimensions. SIAM J. Numer. Anal. 47, 3820–3848 (2009)
    Article MathSciNet Google Scholar
  7. Cockburn, B., Dong, B., Guzmán, J.: A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Math. Comput. 77(264), 1887–1916 (2008)
    Article MathSciNet Google Scholar
  8. Cockburn, B., Gopalakrishnan, J., Lazaron, R.: Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47(2), 1319–1365 (2009)
    Article MathSciNet Google Scholar
  9. Cockburn, B., Gopalakrishnan, J., Sayas, F.-J.: A projection-based error analysis of HDG methods. Math. Comput. 79, 1351–1367 (2010)
    Article MathSciNet Google Scholar
  10. Cui, J., Zhang, W.: An analysis of HDG methods for the Helmholtz equation. IMA J. Numer. Anal. 34(1), 279–295 (2014)
    Article MathSciNet Google Scholar
  11. De Basabe, J.D., Sen, M.K., Wheeler, M.F.: The interior penalty discontinuous Galerkin method for elastic wave propagation: grid dispersion. Geophys. J. Int. 175(1), 83–93 (2014)
    Article Google Scholar
  12. Deraemaeker, A., Babuška, I.M., Bouillard, P.: Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. Int. J. Numer. Meth. Eng. 46(4), 471–499 (1999)
    Article Google Scholar
  13. Giorgiani, G., Fernández-Méndez, S., Huerta, A.: Hybridizable discontinuous Galerkin p-adaptivity for wave propagation problems. Int. J. Numer. Meth. Fluids 72(12), 1244–1262 (2013)
    Article MathSciNet Google Scholar
  14. Gittelson, C.J., Hiptmair, R.: Dispersion analysis of plane wave discontinuous Galerkin methods. Int. J. Numer. Meth. Eng. 98(5), 313–323 (2014)
    Article MathSciNet Google Scholar
  15. Gopalakrishnan, J., Lanteri, S., Olivares, N., Perrusel, R.: Stabilization in relation to wavenumber in HDG methods. Adv. Model. Simul. Eng. Sci. 2(1), 13 (2015)
    Article Google Scholar
  16. Gopalakrishnan, J., Muga, I., Olivares, N.: Dispersive and dissipative errors in the DPG method with scaled norms for the Helmholtz equation. SIAM J. Sci. Comput. 36(1), A20–A39 (2014)
    Article MathSciNet Google Scholar
  17. Griesmaier, R., Monk, P.: Error analysis for a hybridizable discontinuous Galerkin method for the Helmholtz equation. J. Sci. Comput. 49(2), 291–310 (2011)
    Article MathSciNet Google Scholar
  18. Hu, F.Q., Hussaini, M., Rasetarinera, P.: An analysis of the discontinuous Galerkin method for wave propagation problems. J. Comput. Phys. 151(2), 921–946 (1999)
    Article Google Scholar
  19. Kirby, R.C.: Singularity-free evaluation of collapsed-coordinate orthogonal polynomials. ACM Trans. Math. Softw. 37, 5 (2010)
    Article MathSciNet Google Scholar
  20. Sherwin, S.: Dispersion Analysis of the Continuous and Discontinuous Galerkin Formulations, pp. 426–431. Springer Berlin Heidelberg, Berlin, Heidelberg (2000)
    MATH Google Scholar

Download references