Open Access
Volume 53, Number 3, May-June 2019
Page(s) 729 - 747
Published online 05 June 2019
  1. S. Adjerid, A posteriori finite element error estimation for second-order hyperbolic problems. Comput. Methods Appl. Mech. Eng. 191 (2002) 4699–4719. [Google Scholar]
  2. S. Adjerid, A posteriori error estimation for the method of lumped masses applied to second-order hyperbolic problems. Comput. Methods Appl. Mech. Eng. 195 (2006) 4203–4219. [Google Scholar]
  3. S. Adjerid and T.C. Massey, A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems. Comput. Methods Appl. Mech. Eng. 191 (2002) 5877–5897. [Google Scholar]
  4. S. Adjerid and H. Temimi. A discontinuous galerkin method for the wave equation, Comput. Methods Appl. Mech. Eng. 200 (2011) 837–849. [Google Scholar]
  5. G.A. Baker, Error estimates for finite element methods for second order hyperbolic equations. SIAM J. Numer. Anal. 13 (1976) 564–576. [Google Scholar]
  6. W. Bangerth, M. Geiger and R. Rannacher, Adaptive galerkin finite element methods for the wave equation. Comput. Methods Appl. Math. Comput. Methods Appl. Math. 10 (2010) 3–48. [Google Scholar]
  7. W. Bangerth and R. Rannacher, Finite element approximation of the acoustic wave equation: Error control and mesh adaptation. East West J. Numer. Math. 7 (1999) 263–282. [Google Scholar]
  8. W. Bangerth and R. Rannacher, Adaptive finite element techniques for the acoustic wave equation. J. Comput. Acoust. 9 (2001) 575–591. [CrossRef] [MathSciNet] [Google Scholar]
  9. C. Bernardi and E. Süli, Time and space adaptivity for the second-order wave equation. Math. Models Methods Appl. Sci. 15 (2005) 199–225. [Google Scholar]
  10. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. Springer, New York, NY (2004). [CrossRef] [Google Scholar]
  11. L.C. Evans, Partial Differential Equations. American Mathematical Society, Providence, RI (2010). [Google Scholar]
  12. E.H. Georgoulis, O. Lakkis and C. Makridakis, A posteriori L (L2)-error bounds for finite element approximations to the wave equation. IMA J. Numer. Anal. 33 (2013) 1245–1264. [CrossRef] [Google Scholar]
  13. E.H. Georgoulis, O. Lakkis, C.G. Makridakis and J.M. Virtanen, A posteriori error estimates for leap-frog and cosine methods for second order evolution problems. SIAM J. Numer. Anal. 54 (2016) 120–136. [Google Scholar]
  14. O. Gorynina, Eléments finis adaptatifs pour l’équation des ondes instationnaire. Ph.D. thesis, Université de Bourgogne Franche-Comté (2018). [Google Scholar]
  15. O. Gorynina, A. Lozinski and M. Picasso, Time and space adaptivity of the wave equation discretized in time by a second order scheme. IMA J. Numer. Anal. (2018) doi: 10.1093/imanum/dry048. [Google Scholar]
  16. F. Hecht, New development in freefem++. J. Numer. Math. 20 (2012) 251–266. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Lozinski, M. Picasso and V. Prachittham, An anisotropic error estimator for the Crank-Nicolson method: application to a parabolic problem. SIAM J. Sci. Comput. 31 (2009) 2757–2783. [Google Scholar]
  18. N.M. Newmark, A method of computation for structural dynamics. J. Eng. Mech. Div. 85 (1959) 67–94. [Google Scholar]
  19. P.-A. Raviart and J.-M. Thomas, Introduction à l’analyse numérique des équations aux dérivées partielles. Collection Mathématiques Appliquées pour la Maitrise [Collection of Applied Mathematics for the Master’s Degree], Masson, Paris (1983). [Google Scholar]
  20. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [CrossRef] [MathSciNet] [Google Scholar]

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