Free access
Issue
ESAIM: M2AN
Volume 42, Number 6, November-December 2008
Page(s) 925 - 940
DOI http://dx.doi.org/10.1051/m2an:2008033
Published online 12 August 2008
  1. M. Ainsworth, P. Monk and W. Muniz, Dispersive and dissipative properties of discontinuous Galerkin methods for the wave equation. J. Sci. Comput. 27 (2006) 5–40. [CrossRef] [MathSciNet]
  2. D. Arnold, F. Brezzi, B. Cockburn and L. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2002) 1749–1779. [CrossRef] [MathSciNet]
  3. A. Barnett and T. Betcke, Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains. J. Comp. Phys. (to appear).
  4. T. Betcke, A GSVD formulation of a domain decomposition method for planar eigenvalue problems. IMA J. Numer. Anal. 27 (2007) 451–478. [CrossRef] [MathSciNet]
  5. O. Cessenat, Application d'une nouvelle formulation variationnelle aux équations d'ondes harmoniques. Problèmes de Helmholtz 2D et de Maxwell 3D. Ph.D. thesis, Université Paris IX Dauphine, France (1996).
  6. O. Cessenat and B. Després, Application of the ultra-weak variational formulation of elliptic PDEs to the 2-dimensional Helmholtz problem. SIAM J. Numer. Anal. 35 (1998) 255–299. [CrossRef] [MathSciNet]
  7. O. Cessenat and B. Després, Using plane waves as base functions for solving time harmonic equations with the Ultra Weak Variational Formulation. J. Comput. Acoustics 11 (2003) 227–238. [CrossRef]
  8. P. Cummings and X. Feng, Sharp regularity coefficient estimates for complex-valued acoustic and elastic Helmholtz equations. Math. Models Methods Appl. Sci. 16 (2006) 139–160. [CrossRef] [MathSciNet]
  9. P. Gamallo and R. Astley, A comparison of two Trefftz-type methods: The ultraweak variational formulation and the least-squares method, for solving shortwave 2-D Helmholtz problems. Int. J. Numer. Meth. Eng. 71 (2007) 406–432. [CrossRef]
  10. C. Gittelson, R. Hiptmair and I. Perugia, Plane wave discontinuous Galerkin methods. Preprint NI07088-HOP, Isaac Newton Institute Cambride, Cambridge, UK, December (2007) http://www.newton.cam.ac.uk/preprints/NI07088.pdf.
  11. I. Herrera, Boundary Methods: an Algebraic Theory. Pitman (1984).
  12. T. Huttunen, J. Kaipio and P. Monk, The perfectly matched layer for the ultra weak variational formulation of the 3D Helmholtz equation. Int. J. Numer. Meth. Eng. 61 (2004) 1072–1092. [CrossRef]
  13. T. Huttunen, P. Monk and J. Kaipio, Computational aspects of the Ultra Weak Variational Formulation. J. Comput. Phys. 182 (2002) 27–46. [CrossRef] [MathSciNet]
  14. T. Huttunen, P. Monk, F. Collino and J. Kaipio, The Ultra Weak Variational Formulation for elastic wave problems. SIAM J. Sci. Comput. 25 (2004) 1717–1742. [CrossRef] [MathSciNet]
  15. T. Huttunen, M. Malinen and P. Monk, Solving Maxwell's equations using the Ultra Weak Variational Formulation. J. Comput. Phys. 223 (2007) 731–758. [CrossRef] [MathSciNet]
  16. J. Melenk, On generalized finite element methods. Ph.D. thesis, University of Maryland, College Park, USA (1995).
  17. J. Melenk and I. Babuška, The partition of unity finite element method: Basic theory and applications. Comput. Meth. Appl. Mech. Eng. 139 (1996) 289–314. [CrossRef] [MathSciNet]
  18. P. Monk and D. Wang, A least squares method for the Helmholtz equation. Comput. Meth. Appl. Mech. Eng. 175 (1999) 121–136. [CrossRef] [MathSciNet]
  19. M. Stojek, Least-squares Trefftz-type elements for the Helmholtz equation. Int. J. Numer. Meth. Eng. 41 (1998) 831–849. [CrossRef]
  20. R. Tezaur and C. Farhat, Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems. Int. J. Numer. Meth. Eng. 66 (2006) 796–815. [CrossRef]
  21. E. Trefftz, Ein gegenstück zum Ritz'schen verfahren, in Proc. 2nd Int. Congr. Appl. Mech., Zurich (1926) 131–137.

Recommended for you